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Volumn 51, Issue 6, 1996, Pages 1127-1190

The problem of convexity of Chebyshev sets

(2)  Balaganskii, V S a   Vlasov, L P a  

a NONE

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0039466372     PISSN: 00360279     EISSN: 14684829     Source Type: Journal    
DOI: 10.1070/RM1996v051n06ABEH003002     Document Type: Article
Times cited : (56)

References (192)
  • 4
    • 0041173142 scopus 로고
    • Support properties of sets in banach spaces and chebyshev sets
    • N. V. Efimov and S. B. Stechkin, "Support properties of sets in Banach spaces and Chebyshev sets", Dokl. Akad. Nauk. SSSR 127 (1959), 254-257.
    • (1959) Dokl. Akad. Nauk. SSSR , vol.127 , pp. 254-257
    • Efimov, N.V.1    Stechkin, S.B.2
  • 5
    • 0041173143 scopus 로고
    • Approximate compactness and chebyshev sets
    • N. V. Efimov and S. B. Stechkin, "Approximate compactness and Chebyshev sets", Dokl. Akad. Nauk. SSSR 140 (1961), 522-524; English transl. in Soviet Math. Dokl. 2 (1961).
    • (1961) Dokl. Akad. Nauk. SSSR , vol.140 , pp. 522-524
    • Efimov, N.V.1    Stechkin, S.B.2
  • 6
    • 85164654072 scopus 로고
    • N. V. Efimov and S. B. Stechkin, "Approximate compactness and Chebyshev sets", Dokl. Akad. Nauk. SSSR 140 (1961), 522-524; English transl. in Soviet Math. Dokl. 2 (1961).
    • (1961) Soviet Math. Dokl. , vol.2
  • 7
    • 0002972319 scopus 로고
    • Approximation properties of sets in linear normed spaces
    • S. B. Stechkin, "Approximation properties of sets in linear normed spaces", Rev. Math. Pure Appl. 8:1 (1963), 5-18.
    • (1963) Rev. Math. Pure Appl. , vol.8 , Issue.1 , pp. 5-18
    • Stechkin, S.B.1
  • 8
    • 0002456682 scopus 로고
    • Approximative properties of sets in normed linear spaces
    • L. P. Vlasov, "Approximative properties of sets in normed linear spaces", Uspekhi Mat. Nauk 28:6 (1973), 3-66; English transl. in Russian Math. Surveys 28:6 (1973).
    • (1973) Uspekhi Mat. Nauk , vol.28 , Issue.6 , pp. 3-66
    • Vlasov, L.P.1
  • 9
    • 85164655498 scopus 로고
    • L. P. Vlasov, "Approximative properties of sets in normed linear spaces", Uspekhi Mat. Nauk 28:6 (1973), 3-66; English transl. in Russian Math. Surveys 28:6 (1973).
    • (1973) Russian Math. Surveys , vol.28 , Issue.6
  • 10
    • 85164649703 scopus 로고
    • Approximative-geometric properties of sets in banach spaces
    • Preprint, Sverdlovsk
    • V. S. Balaganskii and L. P. Vlasov, "Approximative-geometric properties of sets in Banach spaces", Preprint, Akad. Nauk SSSR Ural. Otdel., Sverdlovsk 1990.
    • (1990) Akad. Nauk SSSR Ural. Otdel.
    • Balaganskii, V.S.1    Vlasov, L.P.2
  • 11
    • 0040578937 scopus 로고
    • A number of connected components of sun's complement
    • A. R. Alimov, "A number of connected components of sun's complement", East J. Approx. 1 (1995), 409-419.
    • (1995) East J. Approx. , vol.1 , pp. 409-419
    • Alimov, A.R.1
  • 12
    • 85164652623 scopus 로고    scopus 로고
    • Complements of chebyshev sets
    • Kaluga 1996, Abstracts of lectures
    • A. R. Alimov, "Complements of Chebyshev sets", Internat. Conf. on the theory of approximation, Kaluga 1996, Abstracts of lectures, Vol. 1, 1996, pp. 10-11.
    • (1996) Internat. Conf. on the Theory of Approximation , vol.1 , pp. 10-11
    • Alimov, A.R.1
  • 13
    • 33748488165 scopus 로고
    • Chebyshev sets in linear spaces with unsymmetric sphere
    • Izdat. Saratov. Univ., (Russian)
    • A. R. Alimov, "Chebyshev sets in linear spaces with unsymmetric sphere", Proc. 7th Saratov Winter School, 1994, Vol. 2, Izdat. Saratov. Univ., 1995, pp. 91-93. (Russian)
    • (1994) Proc. 7th Saratov Winter School , vol.2 , pp. 91-93
    • Alimov, A.R.1
  • 14
    • 0039393815 scopus 로고    scopus 로고
    • Chebyshev set's complement
    • A. R. Alimov, "Chebyshev set's complement", East J. Approx. 2 (1996), 215-232.
    • (1996) East J. Approx. , vol.2 , pp. 215-232
    • Alimov, A.R.1
  • 15
    • 85164653185 scopus 로고
    • 1 (S, Σ, μ)
    • Proc. Internat. Conf., Kaluga Nauka, Moscow (Russian)
    • 1 (S, Σ, μ)", in: Theory of the approximation of functions (Proc. Internat. Conf., Kaluga 1975), Nauka, Moscow 1977, pp. 13-20. (Russian)
    • (1975) Theory of the Approximation of Functions , pp. 13-20
    • Andreev, V.I.1
  • 16
    • 0040578927 scopus 로고
    • The existence of discontinuous metric projections
    • V. I. Andreev, "The existence of discontinuous metric projections", Mat. Zametki 16 (1974), 857-864; English transl. in Math. Notes 16 (1974).
    • (1974) Mat. Zametki , vol.16 , pp. 857-864
    • Andreev, V.I.1
  • 17
    • 85164651792 scopus 로고
    • V. I. Andreev, "The existence of discontinuous metric projections", Mat. Zametki 16 (1974), 857-864; English transl. in Math. Notes 16 (1974).
    • (1974) Math. Notes , vol.16
  • 18
    • 84968515662 scopus 로고
    • Chebyshev sets in Hilbert space
    • E. Asplund, "Chebyshev sets in Hilbert space", Trans. Amer. Math. Soc. 144 (1969), 235-240.
    • (1969) Trans. Amer. Math. Soc. , vol.144 , pp. 235-240
    • Asplund, E.1
  • 20
    • 0040578968 scopus 로고
    • Approximation properties of sets in Hilbert space
    • V. S. Balaganskii, "Approximation properties of sets in Hilbert space", Mat. Zametki 31 (1982), 785-800; English transl. in Math. Notes 31 (1982).
    • (1982) Mat. Zametki , vol.31 , pp. 785-800
    • Balaganskii, V.S.1
  • 21
    • 85164641605 scopus 로고
    • V. S. Balaganskii, "Approximation properties of sets in Hilbert space", Mat. Zametki 31 (1982), 785-800; English transl. in Math. Notes 31 (1982).
    • (1982) Math. Notes , vol.31
  • 22
    • 0039393844 scopus 로고
    • Fréchet differentiability of the distance function, and the structure of a set
    • V. S. Balaganskii, "Fréchet differentiability of the distance function, and the structure of a set", Mat. Zametki 44 (1988), 725-734; English transl. in Math. Notes 44 (1988).
    • (1988) Mat. Zametki , vol.44 , pp. 725-734
    • Balaganskii, V.S.1
  • 23
    • 85164650182 scopus 로고
    • V. S. Balaganskii, "Fréchet differentiability of the distance function, and the structure of a set", Mat. Zametki 44 (1988), 725-734; English transl. in Math. Notes 44 (1988).
    • (1988) Math. Notes , vol.44
  • 24
    • 0040578966 scopus 로고
    • Sufficient conditions for the differentiability of the metric function
    • Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg (Russian)
    • V. S. Balaganskii, "Sufficient conditions for the differentiability of the metric function", in: Proceedings of the Institute of Mathematics and Mechanics, Vol.1, Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg 1992, pp. 84-89. (Russian)
    • (1992) Proceedings of the Institute of Mathematics and Mechanics , vol.1 , pp. 84-89
    • Balaganskii, V.S.1
  • 26
    • 85164648832 scopus 로고    scopus 로고
    • Chebyshev sets with convex complement
    • Akad. Nauk SSSR, Ural. Nauchn. Tsentr, Sverdlovsk (Russian)
    • V. S. Balaganskii, "Chebyshev sets with convex complement", in: Approximation of functions by polynomials and splines, Akad. Nauk SSSR, Ural. Nauchn. Tsentr, Sverdlovsk 1985, pp. 54-57. (Russian)
    • Approximation of Functions by Polynomials and Splines , vol.1985 , pp. 54-57
    • Balaganskii, V.S.1
  • 27
    • 0013475574 scopus 로고
    • On the connection between approximation and geometric properties of sets
    • Akad. Nauk SSSR, Ural. Nauchn. Tsentr, Sverdlovsk (Russian)
    • V. S. Balaganskii, "On the connection between approximation and geometric properties of sets", in: Approximation in concrete and abstract Banach spaces, Akad. Nauk SSSR, Ural. Nauchn. Tsentr, Sverdlovsk 1987, pp. 46-53. (Russian)
    • (1987) Approximation in Concrete and Abstract Banach Spaces , pp. 46-53
    • Balaganskii, V.S.1
  • 28
    • 85164655266 scopus 로고
    • Weak openness of the metric projection
    • V. S. Balaganskii, "Weak openness of the metric projection", Mat. Zametki 49 (1991), 135-144; English transl. in Math. Notes 49 (1991).
    • (1991) Mat. Zametki , vol.49 , pp. 135-144
    • Balaganskii, V.S.1
  • 29
    • 85164632518 scopus 로고
    • V. S. Balaganskii, "Weak openness of the metric projection", Mat. Zametki 49 (1991), 135-144; English transl. in Math. Notes 49 (1991).
    • (1991) Math. Notes , vol.49
  • 30
    • 0039393803 scopus 로고
    • Approximation properties of sets with a convex complement
    • V. S. Balaganskii, "Approximation properties of sets with a convex complement", Mat. Zametki 57 (1995), 20-29; English transl. in Math. Notes 57 (1995).
    • (1995) Mat. Zametki , vol.57 , pp. 20-29
    • Balaganskii, V.S.1
  • 31
    • 85164656919 scopus 로고
    • V. S. Balaganskii, "Approximation properties of sets with a convex complement", Mat. Zametki 57 (1995), 20-29; English transl. in Math. Notes 57 (1995).
    • (1995) Math. Notes , vol.57
  • 32
    • 0013474784 scopus 로고    scopus 로고
    • On the connectedness of the set of points of discontinuity of the metric projection
    • V. S. Balaganskii, "On the connectedness of the set of points of discontinuity of the metric projection", East J. Approx. 2 (1996), 263-279.
    • (1996) East J. Approx. , vol.2 , pp. 263-279
    • Balaganskii, V.S.1
  • 33
    • 85164650633 scopus 로고    scopus 로고
    • Antiproximal sets in spaces of continuous functions
    • to appear
    • V. S. Balaganskii, "Antiproximal sets in spaces of continuous functions", Mat. Zametki (to appear).
    • Mat. Zametki
    • Balaganskii, V.S.1
  • 34
    • 84973564293 scopus 로고    scopus 로고
    • An antiproximal set in a strictly convex space with fréchet differentiable norm
    • V. S. Balaganskii, "An antiproximal set in a strictly convex space with Fréchet differentiable norm", East J. Approx. 2 (1996), 169-176.
    • (1996) East J. Approx. , vol.2 , pp. 169-176
    • Balaganskii, V.S.1
  • 35
    • 0040578934 scopus 로고
    • Weak continuity of a metric projection
    • V. S. Balaganskii, "Weak continuity of a metric projection", Mat. Zametki 22 (1977), 345-356; English transl. in Math. Notes 22 (1977).
    • (1977) Mat. Zametki , vol.22 , pp. 345-356
    • Balaganskii, V.S.1
  • 36
    • 85164656937 scopus 로고
    • V. S. Balaganskii, "Weak continuity of a metric projection", Mat. Zametki 22 (1977), 345-356; English transl. in Math. Notes 22 (1977).
    • (1977) Math. Notes , vol.22
  • 37
    • 0040578967 scopus 로고
    • Weak continuity of the metric projection in banach spaces
    • V. S. Balaganskii, "Weak continuity of the metric projection in Banach spaces", Mat. Zametki 24 (1978), 649-660; English transl. in Math. Notes 24 (1978).
    • (1978) Mat. Zametki , vol.24 , pp. 649-660
    • Balaganskii, V.S.1
  • 38
    • 85164644524 scopus 로고
    • V. S. Balaganskii, "Weak continuity of the metric projection in Banach spaces", Mat. Zametki 24 (1978), 649-660; English transl. in Math. Notes 24 (1978).
    • (1978) Math. Notes , vol.24
  • 39
    • 0040578936 scopus 로고
    • p(μ)"
    • p(μ)", Mat. Zametki 28 (1980), 821-832; English transl. in Math. Notes 28 (1980).
    • (1980) Mat. Zametki , vol.28 , pp. 821-832
    • Balaganskii, V.S.1
  • 40
    • 85164644299 scopus 로고
    • p(μ)", Mat. Zametki 28 (1980), 821-832; English transl. in Math. Notes 28 (1980).
    • (1980) Math. Notes , vol.28
  • 41
    • 0040578928 scopus 로고
    • Weak continuity of the metric projection on bounded sets in banach spaces
    • V. S. Balaganskii, "Weak continuity of the metric projection on bounded sets in Banach spaces", Mat. Zametki 32 (1982), 627-637; English transl. in Math. Notes 32 (1982).
    • (1982) Mat. Zametki , vol.32 , pp. 627-637
    • Balaganskii, V.S.1
  • 42
    • 85164635469 scopus 로고
    • V. S. Balaganskii, "Weak continuity of the metric projection on bounded sets in Banach spaces", Mat. Zametki 32 (1982), 627-637; English transl. in Math. Notes 32 (1982).
    • (1982) Math. Notes , vol.32
  • 43
    • 0040578938 scopus 로고
    • Weak continuity of the metric projection onto weakly compact sets
    • Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg (Russian)
    • V. S. Balaganskii, "Weak continuity of the metric projection onto weakly compact sets", in: Proceedings of the Institute of Mathematics and Mechanics, Vol. 2, Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg 1992, pp. 42-56. (Russian)
    • (1992) Proceedings of the Institute of Mathematics and Mechanics , vol.2 , pp. 42-56
    • Balaganskii, V.S.1
  • 44
    • 0039985993 scopus 로고
    • Weak continuity of the metric projection onto subspaces
    • Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg (Russian)
    • V. S. Balaganskii, "Weak continuity of the metric projection onto subspaces", in: Proceedings of the Institute of Mathematics and Mechanics, Vol. 3, Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg 1995, pp. 80-87. (Russian)
    • (1995) Proceedings of the Institute of Mathematics and Mechanics , vol.3 , pp. 80-87
    • Balaganskii, V.S.1
  • 46
    • 0005789252 scopus 로고
    • Stability of the minimization problem under perturbation of the set of admissible elements
    • V. I. Berdyshev, "Stability of the minimization problem under perturbation of the set of admissible elements", Mat. Sb. 103 (1977), 467-479; English transl. in Math. USSR-Sb. 32 (1977).
    • (1977) Mat. Sb. , vol.103 , pp. 467-479
    • Berdyshev, V.I.1
  • 47
    • 85164634483 scopus 로고
    • V. I. Berdyshev, "Stability of the minimization problem under perturbation of the set of admissible elements", Mat. Sb. 103 (1977), 467-479; English transl. in Math. USSR-Sb. 32 (1977).
    • (1977) Math. USSR-Sb. , vol.32
  • 49
    • 0013519650 scopus 로고
    • Best approximation in Hilbert space
    • Academic Press, New York
    • H. Berens, "Best approximation in Hilbert space", in: Approximation Theory III, Academic Press, New York 1980, pp. 1-20.
    • (1980) Approximation Theory , vol.3 , pp. 1-20
    • Berens, H.1
  • 51
    • 0013545014 scopus 로고
    • Kodissipative metrische projektionen in normierten linearen räumen"
    • Birkhäuser, Basel
    • H. Berens and U. Westphal, "Kodissipative metrische Projektionen in normierten linearen Räumen", in: Linear spaces and approximation, Vol. 40, Birkhäuser, Basel 1978, pp. 119-130.
    • (1978) Linear Spaces and Approximation , vol.40 , pp. 119-130
    • Berens, H.1    Westphal, U.2
  • 53
    • 0002352048 scopus 로고
    • The support functionals of a convex set
    • Amer. Math. Soc., Providence, RI
    • E. Bishop and R. R. Phelps, "The support functionals of a convex set", in: Proc. Symp. Pure Math., Vol. VII, Amer. Math. Soc., Providence, RI 1963, pp. 27-35.
    • (1963) Proc. Symp. Pure Math. , vol.7 , pp. 27-35
    • Bishop, E.1    Phelps, R.R.2
  • 54
    • 0001468398 scopus 로고
    • The differentiability of real functions on normed linear space using generalized subgradients
    • J. M. Borwein, S. P. Fitzpatrick, and J. R. Giles, "The differentiability of real functions on normed linear space using generalized subgradients", Math. Anal. Appl. 128 (1987), 512-534.
    • (1987) Math. Anal. Appl. , vol.128 , pp. 512-534
    • Borwein, J.M.1    Fitzpatrick, S.P.2    Giles, J.R.3
  • 60
    • 0011993169 scopus 로고
    • Chebyshev sets and facial systems of convex sets in finite-dimensional spaces
    • A. L. Brown, "Chebyshev sets and facial systems of convex sets in finite-dimensional spaces", Proc. London Math. Soc. 41 (1980), 297-339.
    • (1980) Proc. London Math. Soc. , vol.41 , pp. 297-339
    • Brown, A.L.1
  • 61
    • 0042091495 scopus 로고
    • Chebyshev sets and the shapes of convex bodies
    • Methods of functional analysis in approximation theory, Bombay Birkhäuser, Basel
    • A. L. Brown, "Chebyshev sets and the shapes of convex bodies", in: Methods of functional analysis in approximation theory, Proc. Internat. Conf., Indian Inst. Techn. Bombay 1985, Birkhäuser, Basel 1986, pp. 97-121.
    • (1985) Proc. Internat. Conf., Indian Inst. Techn. , pp. 97-121
    • Brown, A.L.1
  • 62
    • 0040578915 scopus 로고
    • Suns in normed linear spaces which are finite dimensional
    • A. L. Brown, "Suns in normed linear spaces which are finite dimensional", Math. Ann. 279 (1987), 87-101.
    • (1987) Math. Ann. , vol.279 , pp. 87-101
    • Brown, A.L.1
  • 63
    • 0041173094 scopus 로고
    • On the connectedness properties of suns in finite dimensional spaces
    • A. L. Brown, "On the connectedness properties of suns in finite dimensional spaces", in: Proc. Centre Math. Analysis Austral. Nat. Univ., Vol. 20, 1988, pp. 1-15.
    • (1988) Proc. Centre Math. Analysis Austral. Nat. Univ. , vol.20 , pp. 1-15
    • Brown, A.L.1
  • 65
    • 0039393818 scopus 로고
    • A motzkin-type theorem for closed nonconvex sets
    • L. Calabi and W. E. Hartnett, "A Motzkin-type theorem for closed nonconvex sets", Proc. Amer. Math. Soc. 19 (1968), 1495-1498.
    • (1968) Proc. Amer. Math. Soc. , vol.19 , pp. 1495-1498
    • Calabi, L.1    Hartnett, W.E.2
  • 67
    • 0039985991 scopus 로고
    • Rotundity
    • Amer. Math. Soc., Providence, RI
    • D. F. Cudia, "Rotundity", in: Proc. Sympos. Pure Math., Vol. VII, Amer. Math. Soc., Providence, RI 1963, pp. 73-97.
    • (1963) Proc. Sympos. Pure Math. , vol.7 , pp. 73-97
    • Cudia, D.F.1
  • 68
    • 0004186840 scopus 로고
    • 2nd printing, Academic Press, New York, Springer-Verlag, Berlin-Gottingen-Heidelberg Russian transl. of 1st printing, IL, Moscow
    • M. M. Day, Normed linear spaces, 2nd printing, Academic Press, New York, Springer-Verlag, Berlin-Gottingen-Heidelberg 1962; Russian transl. of 1st printing, IL, Moscow 1961.
    • (1961) Normed Linear Spaces
    • Day, M.M.1
  • 69
    • 0041173115 scopus 로고
    • Existence of best approximations
    • F. Deutsch, "Existence of best approximations", J. Approx. Theory 28 (1980), 132-154.
    • (1980) J. Approx. Theory , vol.28 , pp. 132-154
    • Deutsch, F.1
  • 71
    • 0005335695 scopus 로고
    • A survey of metric selections
    • F. Deutsch, "A survey of metric selections", Contemp. Math. 18 (1983), 49-71.
    • (1983) Contemp. Math. , vol.18 , pp. 49-71
    • Deutsch, F.1
  • 72
    • 0041173110 scopus 로고
    • Selections for metric projections
    • Approximation theory, spline functions and applications Maratea Kluwer Acad. Publ., Dordrecht
    • F. Deutsch, "Selections for metric projections", in: Approximation theory, spline functions and applications (Maratea 1991) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 356, Kluwer Acad. Publ., Dordrecht 1992, pp. 123-137.
    • (1991) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. , vol.356 , pp. 123-137
    • Deutsch, F.1
  • 73
    • 0000704532 scopus 로고
    • Continuous selections and approximate selections for set-valued mappings and applications to metric projections
    • F. Deutsch and P. Kenderov, "Continuous selections and approximate selections for set-valued mappings and applications to metric projections", SIAM J. Math. Anal. 14 (1983), 185-194.
    • (1983) SIAM J. Math. Anal. , vol.14 , pp. 185-194
    • Deutsch, F.1    Kenderov, P.2
  • 77
    • 0002202916 scopus 로고
    • Directional differentiability of the distance function
    • S. I. Dudov, "Directional differentiability of the distance function", Mat. Sb. 186:3 (1995), 29-52; English transl. in Sbornik: Math. 84 (1995).
    • (1995) Mat. Sb. , vol.186 , Issue.3 , pp. 29-52
    • Dudov, S.I.1
  • 78
    • 85164654917 scopus 로고
    • S. I. Dudov, "Directional differentiability of the distance function", Mat. Sb. 186:3 (1995), 29-52; English transl. in Sbornik: Math. 84 (1995).
    • (1995) Sbornik: Math. , vol.84
  • 79
    • 0041173101 scopus 로고
    • Chebyshev sets in C[0, 1] which are not suns
    • C. B. Dunham, "Chebyshev sets in C[0, 1] which are not suns", Canad. Math. Bull. (1) 18 (1975), 35-37.
    • (1975) Canad. Math. Bull. (1) , vol.18 , pp. 35-37
    • Dunham, C.B.1
  • 81
    • 84971179618 scopus 로고
    • Metric projections and the differentiability of distance functions
    • S. Fitzpatrick, "Metric projections and the differentiability of distance functions", Bull. Austral. Math. Soc. 22 (1980), 291-312.
    • (1980) Bull. Austral. Math. Soc. , vol.22 , pp. 291-312
    • Fitzpatrick, S.1
  • 82
    • 84968469796 scopus 로고
    • Differentiation of real-valued functions and continuity of metric projections
    • S. Fitzpatrick, "Differentiation of real-valued functions and continuity of metric projections", Proc. Amer. Math. Soc. 91 (1984), 544-548.
    • (1984) Proc. Amer. Math. Soc. , vol.91 , pp. 544-548
    • Fitzpatrick, S.1
  • 83
    • 84971160267 scopus 로고
    • Approximation properties of sets with bounded complements
    • C. Franchetti and P. L. Papini, "Approximation properties of sets with bounded complements", Proc. Roy. Soc. Edinburgh Sect. A 89 (1981), 75-86.
    • (1981) Proc. Roy. Soc. Edinburgh Sect. A , vol.89 , pp. 75-86
    • Franchetti, C.1    Papini, P.L.2
  • 84
    • 0003486420 scopus 로고
    • Convex analysis with application in differentiation of convex functions
    • Pitman, Boston-London
    • J. R. Giles, Convex analysis with application in differentiation of convex functions, Research Notes in Math., 58, Pitman, Boston-London 1982.
    • (1982) Research Notes in Math. , vol.58
    • Giles, J.R.1
  • 85
    • 0040578935 scopus 로고
    • On a problem of H. Berens
    • G. Godini, "On a problem of H. Berens", Math. Ann. 263 (1983), 279-281.
    • (1983) Math. Ann. , vol.263 , pp. 279-281
    • Godini, G.1
  • 86
    • 84915829909 scopus 로고
    • Dissertation, Univ. Erlangen-Nürnberg
    • n, Dissertation, Univ. Erlangen-Nürnberg 1981.
    • (1981) n
    • Hetzelt, L.1
  • 87
    • 0041173093 scopus 로고
    • On suns and cosuns in finite dimensional normed real vector spaces
    • L. Hetzelt, "On suns and cosuns in finite dimensional normed real vector spaces", Acta Math. Hungar. 45 (1985), 53-68.
    • (1985) Acta Math. Hungar. , vol.45 , pp. 53-68
    • Hetzelt, L.1
  • 88
    • 0002798456 scopus 로고
    • New concepts in nondifferentiable programming
    • J-B. Hiriart-Urruty, "New concepts in nondifferentiable programming", Bull. Soc. Math. France 60 (1979), 57-85.
    • (1979) Bull. Soc. Math. France , vol.60 , pp. 57-85
    • Hiriart-Urruty, J.-B.1
  • 90
    • 84915843689 scopus 로고
    • On the continuity of the best approximation operators
    • R. B. Holmes, "On the continuity of the best approximation operators", Ann. Math. Stud. 69 (1972), 137-157.
    • (1972) Ann. Math. Stud. , vol.69 , pp. 137-157
    • Holmes, R.B.1
  • 94
    • 38249000931 scopus 로고
    • On Johnson's example of a nonconvex chebyshev set
    • M. Jiang, "On Johnson's example of a nonconvex Chebyshev set", J. Approx. Theory 74 (1993), 152-158.
    • (1993) J. Approx. Theory , vol.74 , pp. 152-158
    • Jiang, M.1
  • 95
    • 38249033425 scopus 로고
    • A nonconvex set which has the unique nearest point property
    • G. G. Johnson, "A nonconvex set which has the unique nearest point property", J. Approx. Theory 51 (1987), 289-332.
    • (1987) J. Approx. Theory , vol.51 , pp. 289-332
    • Johnson, G.G.1
  • 96
    • 85164642779 scopus 로고
    • Nontrivial chebyshev sets on compact connected manifolds
    • M. I. Karlov, "Nontrivial Chebyshev sets on compact connected manifolds", East J. Approx. 1 (1995), 527-542.
    • (1995) East J. Approx. , vol.1 , pp. 527-542
    • Karlov, M.I.1
  • 97
    • 85164636732 scopus 로고
    • Approximation properties of curves in Hilbert space
    • Izdat. Saratov. Univ., Saratov
    • M. I. Karlov, "Approximation properties of curves in Hilbert space", Proc. 7th Saratov Winter School, 1994, Vol. 3, Izdat. Saratov. Univ., Saratov 1995, pp. 13-16.
    • (1994) Proc. 7th Saratov Winter School , vol.3 , pp. 13-16
    • Karlov, M.I.1
  • 98
    • 85164644490 scopus 로고    scopus 로고
    • 2-manifolds in Hilbert space
    • Kaluga 1996, Abstracts of lectures
    • 2-manifolds in Hilbert space", Internat. Conf. on Theory of Approximation, Kaluga 1996, Abstracts of lectures, Vol. 1, 1996, pp. 112-113.
    • (1996) Internat. Conf. on Theory of Approximation , vol.1 , pp. 112-113
    • Karlov, M.I.1
  • 99
    • 0040578870 scopus 로고    scopus 로고
    • 2-manifolds in Hilbert space
    • 2-manifolds in Hilbert space", East J. Approx. 2 (1996), 197-203.
    • (1996) East J. Approx. , vol.2 , pp. 197-203
    • Karlov, M.I.1
  • 101
    • 84961908812 scopus 로고
    • A note on multivalued monotone mappings
    • P. S. Kenderov, "A note on multivalued monotone mappings", C. R. Acad. Bulgare Sci. 28 (1975), 583-584.
    • (1975) C. R. Acad. Bulgare Sci. , vol.28 , pp. 583-584
    • Kenderov, P.S.1
  • 102
    • 0002403480 scopus 로고
    • Dispersed chebyshev sets and coverings by balls
    • V. Klee, "Dispersed Chebyshev sets and coverings by balls", Math. Ann. 257 (1981), 251-260.
    • (1981) Math. Ann. , vol.257 , pp. 251-260
    • Klee, V.1
  • 103
    • 0001185087 scopus 로고
    • Do infinite-dimensional banach spaces admit nice tiling?
    • V. Klee, "Do infinite-dimensional Banach spaces admit nice tiling?", Stud. Sci. Math. Hungar. 21 (1986), 415-427.
    • (1986) Stud. Sci. Math. Hungar. , vol.21 , pp. 415-427
    • Klee, V.1
  • 105
    • 0039985979 scopus 로고
    • Approximation properties of arbitrary sets in banach spaces
    • S. V. Konyagin, "Approximation properties of arbitrary sets in Banach spaces", Dokl. Akad. Nauk SSSR 239 (1978), 261-264; English transl. in Soviet Math. Dokl. 19 (1978).
    • (1978) Dokl. Akad. Nauk SSSR , vol.239 , pp. 261-264
    • Konyagin, S.V.1
  • 106
    • 85164636230 scopus 로고
    • S. V. Konyagin, "Approximation properties of arbitrary sets in Banach spaces", Dokl. Akad. Nauk SSSR 239 (1978), 261-264; English transl. in Soviet Math. Dokl. 19 (1978).
    • (1978) Soviet Math. Dokl. , vol.19
  • 107
    • 0039985967 scopus 로고
    • Approximation properties of closed sets in banach spaces and the characterization of strongly convex spaces
    • S. V. Konyagin, "Approximation properties of closed sets in Banach spaces and the characterization of strongly convex spaces", Dokl. Akad. Nauk SSSR 251 (1980), 276-280; English transl. in Soviet Math. Dokl. 21 (1980).
    • (1980) Dokl. Akad. Nauk SSSR , vol.251 , pp. 276-280
    • Konyagin, S.V.1
  • 108
    • 85164636262 scopus 로고
    • S. V. Konyagin, "Approximation properties of closed sets in Banach spaces and the characterization of strongly convex spaces", Dokl. Akad. Nauk SSSR 251 (1980), 276-280; English transl. in Soviet Math. Dokl. 21 (1980).
    • (1980) Soviet Math. Dokl. , vol.21
  • 109
    • 0013541118 scopus 로고    scopus 로고
    • Set of points of discontinuity of a metric projection on chebyshev sets in Hilbert space
    • Kaluga 1996, Abstracts of lectures
    • S. V. Konyagin, "Set of points of discontinuity of a metric projection on Chebyshev sets in Hilbert space", Internat. Conf. on Theory of Approximation, Kaluga 1996, Abstracts of lectures, Vol. 1, 1996, pp. 120-121.
    • (1996) Internat. Conf. on Theory of Approximation , vol.1 , pp. 120-121
    • Konyagin, S.V.1
  • 110
    • 0002289899 scopus 로고
    • Sets of points of nonemptiness and continuity of a metric projection
    • S. V. Konyagin, "Sets of points of nonemptiness and continuity of a metric projection", Mat. Zametki 33 (1983), 641-655; English transl. in Math. Notes 33 (1983).
    • (1983) Mat. Zametki , vol.33 , pp. 641-655
    • Konyagin, S.V.1
  • 111
    • 85164653694 scopus 로고
    • S. V. Konyagin, "Sets of points of nonemptiness and continuity of a metric projection", Mat. Zametki 33 (1983), 641-655; English transl. in Math. Notes 33 (1983).
    • (1983) Math. Notes , vol.33
  • 112
    • 0039393808 scopus 로고
    • Sets of existence of elements of best approximation
    • Saratov Saratov. Gos. Univ., Saratov (Russian)
    • S. V. Konyagin, "Sets of existence of elements of best approximation", in: Theory of functions and approximations, Part 2 (Saratov 1984), Saratov. Gos. Univ., Saratov 1986, pp. 136-139. (Russian)
    • (1984) Theory of Functions and Approximations, Part 2 , pp. 136-139
    • Konyagin, S.V.1
  • 113
    • 0041173100 scopus 로고
    • Connectedness of sets in problems of best approximation
    • S. V. Konyagin, "Connectedness of sets in problems of best approximation", Dokl. Akad. Nauk SSSR 261 (1981), 20-23; English transl. in Soviet Math. Dokl. 24 (1981).
    • (1981) Dokl. Akad. Nauk SSSR , vol.261 , pp. 20-23
    • Konyagin, S.V.1
  • 114
    • 85164651718 scopus 로고
    • S. V. Konyagin, "Connectedness of sets in problems of best approximation", Dokl. Akad. Nauk SSSR 261 (1981), 20-23; English transl. in Soviet Math. Dokl. 24 (1981).
    • (1981) Soviet Math. Dokl. , vol.24
  • 115
    • 85164653616 scopus 로고    scopus 로고
    • Approximation properties of arbitrary closed sets in banach spaces
    • to appear
    • S. V. Konyagin, "Approximation properties of arbitrary closed sets in Banach spaces", Fundamental and Applied Mathematics (to appear).
    • Fundamental and Applied Mathematics
    • Konyagin, S.V.1
  • 117
    • 85164649659 scopus 로고
    • S. V. Konyagin and I. G. Tsar'kov, "Efimov-Stechkin spaces", Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1986, no. 5, 20-27; English transl. in Moscow Univ. Math. Bull. 41:5 (1986).
    • (1986) Moscow Univ. Math. Bull. , vol.41 , Issue.5
  • 118
    • 0040578905 scopus 로고
    • Connectedness and certain approximation properties of sets in normed linear spaces
    • V. A. Koshcheev, "Connectedness and certain approximation properties of sets in normed linear spaces", Mat. Zametki 17 (1975), 193-204; English transl. in Math. Notes 17 (1975).
    • (1975) Mat. Zametki , vol.17 , pp. 193-204
    • Koshcheev, V.A.1
  • 119
    • 85164633883 scopus 로고
    • V. A. Koshcheev, "Connectedness and certain approximation properties of sets in normed linear spaces", Mat. Zametki 17 (1975), 193-204; English transl. in Math. Notes 17 (1975).
    • (1975) Math. Notes , vol.17
  • 120
    • 0040578911 scopus 로고
    • Connectedness and solar properties of sets in normed linear spaces
    • V. A. Koshcheev, "Connectedness and solar properties of sets in normed linear spaces", Mat. Zametki 19 (1976), 267-278; English transl. in Math. Notes 19 (1976).
    • (1976) Mat. Zametki , vol.19 , pp. 267-278
    • Koshcheev, V.A.1
  • 121
    • 85164655372 scopus 로고
    • V. A. Koshcheev, "Connectedness and solar properties of sets in normed linear spaces", Mat. Zametki 19 (1976), 267-278; English transl. in Math. Notes 19 (1976).
    • (1976) Math. Notes , vol.19
  • 122
    • 85164633466 scopus 로고
    • Connectedness and 'solar' properties of sets in normed linear spaces
    • Proc. Internat. Conf., Kaluga Nauka, Moscow (Russian)
    • V. A. Koshcheev, "Connectedness and 'solar' properties of sets in normed linear spaces", in: Theory of approximation of functions (Proc. Internat. Conf., Kaluga 1975), Nauka, Moscow 1977, pp. 248-250. (Russian)
    • (1975) Theory of Approximation of Functions , pp. 248-250
    • Koshcheev, V.A.1
  • 124
    • 0039985972 scopus 로고
    • An example of a disconnected sun in a banach space
    • V. A. Koshcheev, "An example of a disconnected sun in a Banach space", Mat. Zametki 26 (1979), 89-92; English transl. in Math. Notes 26 (1979).
    • (1979) Mat. Zametki , vol.26 , pp. 89-92
    • Koshcheev, V.A.1
  • 125
    • 85164650308 scopus 로고
    • V. A. Koshcheev, "An example of a disconnected sun in a Banach space", Mat. Zametki 26 (1979), 89-92; English transl. in Math. Notes 26 (1979).
    • (1979) Math. Notes , vol.26
  • 126
    • 0039393798 scopus 로고
    • On the structure of suns in banach spaces
    • Proc. Internat. Conf., Gdańsk North Holland, Amsterdam
    • V. A. Koshcheev, "On the structure of suns in Banach spaces", in: Approximation and function spaces (Proc. Internat. Conf., Gdańsk 1979), North Holland, Amsterdam 1981, pp. 371-376.
    • (1979) Approximation and Function Spaces , pp. 371-376
    • Koshcheev, V.A.1
  • 127
    • 0003391813 scopus 로고
    • Academic Press, New York-London, PWN, Warsaw 1966; Russian transl., Mir, Moscow
    • K. Kuratowski, Topology. Vol. I, Academic Press, New York-London, PWN, Warsaw 1966; Russian transl., Mir, Moscow 1966.
    • (1966) Topology , vol.1
    • Kuratowski, K.1
  • 128
    • 0003391813 scopus 로고
    • Academic Press, New York-London, PWN, Warsaw Russian transl., Mir, Moscow
    • K. Kuratowski, Topology. Vol. II, Academic Press, New York-London, PWN, Warsaw 1968; Russian transl., Mir, Moscow 1969.
    • (1968) Topology , vol.2
    • Kuratowski, K.1
  • 129
    • 0000870344 scopus 로고
    • Almost chebyshev subsets in reflexive banach spaces
    • K.-S. Lau, "Almost Chebyshev subsets in reflexive Banach spaces", Indiana Univ. Math. J. 27 (1978), 791-795.
    • (1978) Indiana Univ. Math. J. , vol.27 , pp. 791-795
    • Lau, K.-S.1
  • 130
    • 85164645018 scopus 로고
    • Continuous selections for metric projections and interpolating subspaces
    • Peter Lang, Frankfurt
    • Wu Li, "Continuous selections for metric projections and interpolating subspaces", in: Approximation and optimization, Vol.1, Peter Lang, Frankfurt 1991, pp. 1-108.
    • (1991) Approximation and Optimization , vol.1 , pp. 1-108
    • Wu, L.1
  • 131
    • 0041173098 scopus 로고
    • Untersuchungen über wabenzellen bei allgemeiner minkowskischer metrik
    • H. Mann, "Untersuchungen über Wabenzellen bei allgemeiner Minkowskischer Metrik", Monatsh. Math. Phys. 42 (1937), 74-83.
    • (1937) Monatsh. Math. Phys. , vol.42 , pp. 74-83
    • Mann, H.1
  • 132
    • 0039393805 scopus 로고
    • Continuity and connectedness of the metric δ-projection
    • Akad. Nauk SSSR, Ural. Nauchn. Tsentr, Sverdlovsk (Russian)
    • A. V. Marinov, "Continuity and connectedness of the metric δ-projection", in: Approximation in concrete and abstract Banach spaces, Akad. Nauk SSSR, Ural. Nauchn. Tsentr, Sverdlovsk 1987, pp. 82-95. (Russian)
    • (1987) Approximation in Concrete and Abstract Banach Spaces , pp. 82-95
    • Marinov, A.V.1
  • 133
    • 85164638972 scopus 로고
    • Estimates for the stability of a metric ε-projection in terms of the modulus of convexity of a space
    • Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg (Russian)
    • A. V. Marinov, "Estimates for the stability of a metric ε-projection in terms of the modulus of convexity of a space", in: Proceedings of the Institute of Mathematics and Mechanics, Vol. 2, Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg 1992, pp. 85-109. (Russian)
    • (1992) Proceedings of the Institute of Mathematics and Mechanics , vol.2 , pp. 85-109
    • Marinov, A.V.1
  • 135
    • 84972577815 scopus 로고
    • Banach spaces which are asplund spaces
    • I. Namioka and R. R. Phelps, "Banach spaces which are Asplund spaces", Duke Math. J. 42 (1975), 735-750.
    • (1975) Duke Math. J. , vol.42 , pp. 735-750
    • Namioka, I.1    Phelps, R.R.2
  • 136
    • 0039985973 scopus 로고
    • A study of farthest points
    • T. D. Narang, "A study of farthest points", Nieuw Arch. Wiskunde (3) 25 (1977), 54-79.
    • (1977) Nieuw Arch. Wiskunde (3) , vol.25 , pp. 54-79
    • Narang, T.D.1
  • 137
    • 0039393779 scopus 로고
    • Convexity of chebyshev sets
    • T. D. Narang, "Convexity of Chebyshev sets", Nieuw Arch. Wiskunde (3) 25 (1977), 377-402.
    • (1977) Nieuw Arch. Wiskunde (3) , vol.25 , pp. 377-402
    • Narang, T.D.1
  • 138
    • 0039985901 scopus 로고
    • Uniquely remotal sets are singletons
    • T. D. Narang, "Uniquely remotal sets are singletons", Nieuw Arch. Wiskunde (4) 9 (1991), 1-12.
    • (1991) Nieuw Arch. Wiskunde (4) , vol.9 , pp. 1-12
    • Narang, T.D.1
  • 139
    • 0039393786 scopus 로고
    • Strict suns and lower semicontinuity of a metric projection in normed linear spaces
    • N. V. Nevesenko, "Strict suns and lower semicontinuity of a metric projection in normed linear spaces", Mat. Zametki 23 (1978), 563-572; English transl. in Math. Notes 23 (1978).
    • (1978) Mat. Zametki , vol.23 , pp. 563-572
    • Nevesenko, N.V.1
  • 140
    • 85164645271 scopus 로고
    • N. V. Nevesenko, "Strict suns and lower semicontinuity of a metric projection in normed linear spaces", Mat. Zametki 23 (1978), 563-572; English transl. in Math. Notes 23 (1978).
    • (1978) Math. Notes , vol.23
  • 141
    • 0039393797 scopus 로고
    • ρ-continuity of the metric projection onto convex closed sets
    • N. V. Nevesenko, "ρ-continuity of the metric projection onto convex closed sets", Mat. Zametki 23 (1978), 845-854; English transl. in Math. Notes 23 (1978).
    • (1978) Mat. Zametki , vol.23 , pp. 845-854
    • Nevesenko, N.V.1
  • 142
    • 85164646253 scopus 로고
    • N. V. Nevesenko, "ρ-continuity of the metric projection onto convex closed sets", Mat. Zametki 23 (1978), 845-854; English transl. in Math. Notes 23 (1978).
    • (1978) Math. Notes , vol.23
  • 143
    • 0041173053 scopus 로고
    • The metric projection and connectedness of sets in normed linear spaces
    • N. V. Nevesenko, "The metric projection and connectedness of sets in normed linear spaces", Izv. Vyssh. Uchebn. Zaved. Mat. 1979, no. 1, 51-53; English transl. in Soviet Math. Iz. VUZ 23 (1979).
    • (1979) Izv. Vyssh. Uchebn. Zaved. Mat. , vol.1 , pp. 51-53
    • Nevesenko, N.V.1
  • 144
    • 85164652712 scopus 로고
    • N. V. Nevesenko, "The metric projection and connectedness of sets in normed linear spaces", Izv. Vyssh. Uchebn. Zaved. Mat. 1979, no. 1, 51-53; English transl. in Soviet Math. Iz. VUZ 23 (1979).
    • (1979) Soviet Math. Iz. VUZ , vol.23
  • 145
    • 0039393736 scopus 로고
    • Metric projection on convex sets
    • N. V. Nevesenko and E. V. Oshman, "Metric projection on convex sets", Mat. Zametki 31 (1982), 117-126; English transl. in Math. Notes 31 (1982).
    • (1982) Mat. Zametki , vol.31 , pp. 117-126
    • Nevesenko, N.V.1    Oshman, E.V.2
  • 146
    • 85164635978 scopus 로고
    • N. V. Nevesenko and E. V. Oshman, "Metric projection on convex sets", Mat. Zametki 31 (1982), 117-126; English transl. in Math. Notes 31 (1982).
    • (1982) Math. Notes , vol.31
  • 147
    • 0013132743 scopus 로고
    • Continuity of the metric projection
    • E. V. Oshman, "Continuity of the metric projection", Mat. Zametki 37 (1985), 200-211; English transl. in Math. Notes 37 (1985).
    • (1985) Mat. Zametki , vol.37 , pp. 200-211
    • Oshman, E.V.1
  • 148
    • 85164649196 scopus 로고
    • E. V. Oshman, "Continuity of the metric projection", Mat. Zametki 37 (1985), 200-211; English transl. in Math. Notes 37 (1985).
    • (1985) Math. Notes , vol.37
  • 149
    • 85164646532 scopus 로고
    • Continuity of mappings connected with minimization of convex functions
    • Ural. Gos. Univ., Sverdlovsk (Russian)
    • E. V. Oshman, "Continuity of mappings connected with minimization of convex functions", in: Investigations in topology and operator theory, Ural. Gos. Univ., Sverdlovsk 1990, pp. 103-108. (Russian)
    • (1990) Investigations in Topology and Operator Theory , pp. 103-108
    • Oshman, E.V.1
  • 150
    • 0039755448 scopus 로고
    • Approximative compactness and continuity of metric projections
    • B. B. Panda and O. P. Kapoor, "Approximative compactness and continuity of metric projections", Bull. Austral. Math. Soc. 11 (1974), 47-55.
    • (1974) Bull. Austral. Math. Soc. , vol.11 , pp. 47-55
    • Panda, B.B.1    Kapoor, O.P.2
  • 151
    • 84966226465 scopus 로고
    • Convex sets and subharmonicity of the distance function
    • M. J. Parker, "Convex sets and subharmonicity of the distance function", Proc. Amer. Math. Soc. 103 (1988), 503-506.
    • (1988) Proc. Amer. Math. Soc. , vol.103 , pp. 503-506
    • Parker, M.J.1
  • 152
    • 0041173083 scopus 로고
    • Support cones and their generalizations
    • Amer. Math. Soc., Providence, RI
    • R. R. Phelps, "Support cones and their generalizations", Proc. Sympos. Pure Math., Vol. VII, Amer. Math. Soc., Providence, RI 1963, 393-401.
    • (1963) Proc. Sympos. Pure Math. , vol.7 , pp. 393-401
    • Phelps, R.R.1
  • 153
    • 0039393778 scopus 로고
    • Openness of metric projection in certain banach spaces
    • R. R. Phelps, "Openness of metric projection in certain Banach spaces", J. Approx. Theory 42 (1984), 70-79.
    • (1984) J. Approx. Theory , vol.42 , pp. 70-79
    • Phelps, R.R.1
  • 154
    • 0039393783 scopus 로고
    • A differential inequality for the distance function in normed linear spaces
    • R. Redheffer and W. Walter, "A differential inequality for the distance function in normed linear spaces", Math. Ann. 211 (1974), 299-314.
    • (1974) Math. Ann. , vol.211 , pp. 299-314
    • Redheffer, R.1    Walter, W.2
  • 155
    • 0004267646 scopus 로고
    • Princeton Univ. Press, Princeton, NJ Russian transl., Mir, Moscow
    • R. T. Rockafeller, Convex analysis, Princeton Univ. Press, Princeton, NJ 1970; Russian transl., Mir, Moscow 1973.
    • (1970) Convex Analysis
    • Rockafeller, R.T.1
  • 158
    • 0010885315 scopus 로고
    • The theory of best approximation and functional analysis
    • Philadelphia, PA
    • I. Singer, The theory of best approximation and functional analysis, SIAM, Philadelphia, PA 1974.
    • (1974) SIAM
    • Singer, I.1
  • 160
    • 0002385538 scopus 로고
    • Ordering and completeness of metric spaces
    • F. Sullivan, "Ordering and completeness of metric spaces", Nieuw Arch. Wiskunde (3) 29 (1981), 178-193.
    • (1981) Nieuw Arch. Wiskunde (3) , vol.29 , pp. 178-193
    • Sullivan, F.1
  • 161
    • 85164655871 scopus 로고
    • Convex analysis. Analysis II
    • Springer-Verlag, Berlin
    • V. Tikhomirov, "Convex Analysis. Analysis II", in: Encyclopedia Math. Sci., Springer-Verlag, Berlin 1990.
    • (1990) Encyclopedia Math. Sci.
    • Tikhomirov, V.1
  • 162
    • 0040578866 scopus 로고
    • Bounded chebyshev sets in finite-dimensional banach spaces
    • I. G. Tsar'kov, "Bounded Chebyshev sets in finite-dimensional Banach spaces", Mat. Zametki 36 (1984), 73-87; English transl. in Math. Notes 36 (1984).
    • (1984) Mat. Zametki , vol.36 , pp. 73-87
    • Tsar'kov, I.G.1
  • 163
    • 85164654620 scopus 로고
    • I. G. Tsar'kov, "Bounded Chebyshev sets in finite-dimensional Banach spaces", Mat. Zametki 36 (1984), 73-87; English transl. in Math. Notes 36 (1984).
    • (1984) Math. Notes , vol.36
  • 164
    • 0039985905 scopus 로고
    • Connectivity of certain classes of sets in banach spaces
    • I. G. Tsar'kov, "Connectivity of certain classes of sets in Banach spaces", Mat. Zametki 40 (1986), 174-196; English transl. in Math. Notes 40 (1986).
    • (1986) Mat. Zametki , vol.40 , pp. 174-196
    • Tsar'kov, I.G.1
  • 165
    • 85164635893 scopus 로고
    • I. G. Tsar'kov, "Connectivity of certain classes of sets in Banach spaces", Mat. Zametki 40 (1986), 174-196; English transl. in Math. Notes 40 (1986).
    • (1986) Math. Notes , vol.40
  • 167
    • 0041173033 scopus 로고
    • Local "homogeneity" of uniqueness sets
    • I. G. Tsar'kov, "Local "homogeneity" of uniqueness sets", Mat. Zametki 45 (1989), 121-123; English transl. in Math. Notes 45 (1989).
    • (1989) Mat. Zametki , vol.45 , pp. 121-123
    • Tsar'kov, I.G.1
  • 168
    • 85164634329 scopus 로고
    • I. G. Tsar'kov, "Local "homogeneity" of uniqueness sets", Mat. Zametki 45 (1989), 121-123; English transl. in Math. Notes 45 (1989).
    • (1989) Math. Notes , vol.45
  • 169
    • 0039985904 scopus 로고
    • Continuity of a metric projection, structural and approximation properties of sets
    • I. G. Tsar'kov, "Continuity of a metric projection, structural and approximation properties of sets", Mat. Zametki 47 (1990), 137-148; English transl. in Math. Notes 47 (1990).
    • (1990) Mat. Zametki , vol.47 , pp. 137-148
    • Tsar'kov, I.G.1
  • 170
    • 85164646284 scopus 로고
    • I. G. Tsar'kov, "Continuity of a metric projection, structural and approximation properties of sets", Mat. Zametki 47 (1990), 137-148; English transl. in Math. Notes 47 (1990).
    • (1990) Math. Notes , vol.47
  • 171
    • 0013512708 scopus 로고
    • A connectedness property of maximal monotone operators and its application to approximation theory
    • L. Veselý, "A connectedness property of maximal monotone operators and its application to approximation theory", Proc. Amer. Math. Soc. 115 (1992), 663-667.
    • (1992) Proc. Amer. Math. Soc. , vol.115 , pp. 663-667
    • Veselý, L.1
  • 172
    • 85164638830 scopus 로고
    • Chebyshev set
    • Moscow (Russian)
    • L. P. Vlasov, "Chebyshev set", in: Math. Encyclopedia, Vol. 5, Moscow 1985. (Russian)
    • (1985) Math. Encyclopedia , vol.5
    • Vlasov, L.P.1
  • 174
    • 0039985949 scopus 로고
    • Approximation properties of sets in banach spaces
    • L. P. Vlasov, "Approximation properties of sets in Banach spaces", Mat. Zametki 7 (1970), 593-604; English transl. in Math. Notes 7 (1970).
    • (1970) Mat. Zametki , vol.7 , pp. 593-604
    • Vlasov, L.P.1
  • 175
    • 85164651966 scopus 로고
    • L. P. Vlasov, "Approximation properties of sets in Banach spaces", Mat. Zametki 7 (1970), 593-604; English transl. in Math. Notes 7 (1970).
    • (1970) Math. Notes , vol.7
  • 176
    • 0041173047 scopus 로고
    • Several theorems on chebyshev sets
    • L. P. Vlasov, "Several theorems on Chebyshev sets", Mat. Zametki 11 (1972), 135-144; English transl. in Math. Notes 11 (1972).
    • (1972) Mat. Zametki , vol.11 , pp. 135-144
    • Vlasov, L.P.1
  • 177
    • 85164653803 scopus 로고
    • L. P. Vlasov, "Several theorems on Chebyshev sets", Mat. Zametki 11 (1972), 135-144; English transl. in Math. Notes 11 (1972).
    • (1972) Math. Notes , vol.11
  • 178
    • 0005879731 scopus 로고
    • The concept of approximate compactness, and its variants
    • L. P. Vlasov, "The concept of approximate compactness, and its variants", Mat. Zametki 16 (1974), 337-348; English transl. in Math. Notes 16 (1974).
    • (1974) Mat. Zametki , vol.16 , pp. 337-348
    • Vlasov, L.P.1
  • 179
    • 85164656477 scopus 로고
    • L. P. Vlasov, "The concept of approximate compactness, and its variants", Mat. Zametki 16 (1974), 337-348; English transl. in Math. Notes 16 (1974).
    • (1974) Math. Notes , vol.16
  • 180
    • 0039985900 scopus 로고
    • Almost convex sets
    • L. P. Vlasov, "Almost convex sets", Mat. Zametki 18 (1975), 343-356; English transl. in Math. Notes 18 (1975).
    • (1975) Mat. Zametki , vol.18 , pp. 343-356
    • Vlasov, L.P.1
  • 181
    • 85164648645 scopus 로고
    • L. P. Vlasov, "Almost convex sets", Mat. Zametki 18 (1975), 343-356; English transl. in Math. Notes 18 (1975).
    • (1975) Math. Notes , vol.18
  • 182
    • 0005790194 scopus 로고
    • Properties of generalized elements of the best approximation
    • L. P. Vlasov, "Properties of generalized elements of the best approximation", Mat. Zametki 24 (1978), 513-522; English transl. in Math. Notes 24 (1978).
    • (1978) Mat. Zametki , vol.24 , pp. 513-522
    • Vlasov, L.P.1
  • 183
    • 85164643379 scopus 로고
    • L. P. Vlasov, "Properties of generalized elements of the best approximation", Mat. Zametki 24 (1978), 513-522; English transl. in Math. Notes 24 (1978).
    • (1978) Math. Notes , vol.24
  • 184
    • 0039393739 scopus 로고
    • On the continuity of a metric projection
    • L. P. Vlasov, "On the continuity of a metric projection", Mat. Zametki 30 (1981), 813-818; English transl. in Math. Notes 30 (1981).
    • (1981) Mat. Zametki , vol.30 , pp. 813-818
    • Vlasov, L.P.1
  • 185
    • 85164648582 scopus 로고
    • L. P. Vlasov, "On the continuity of a metric projection", Mat. Zametki 30 (1981), 813-818; English transl. in Math. Notes 30 (1981).
    • (1981) Math. Notes , vol.30
  • 186
    • 85164637583 scopus 로고
    • Continuity of a metric projection onto convex sets
    • L. P. Vlasov, "Continuity of a metric projection onto convex sets", Mat. Zametki 52:6 (1992), 3-9; English transl. in Math. Notes 52 (1993).
    • (1992) Mat. Zametki , vol.52 , Issue.6 , pp. 3-9
    • Vlasov, L.P.1
  • 187
    • 85164644710 scopus 로고
    • L. P. Vlasov, "Continuity of a metric projection onto convex sets", Mat. Zametki 52:6 (1992), 3-9; English transl. in Math. Notes 52 (1993).
    • (1993) Math. Notes , vol.52
  • 188
    • 84966225327 scopus 로고
    • On a property of metric projections onto closed subsets of Hilbert spaces
    • U. Westphal and J. Frerking, "On a property of metric projections onto closed subsets of Hilbert spaces", Proc. Amer. Math. Soc. 105 (1989), 644-651.
    • (1989) Proc. Amer. Math. Soc. , vol.105 , pp. 644-651
    • Westphal, U.1    Frerking, J.2
  • 189
    • 4243487328 scopus 로고
    • On the points of multivaluedness of metric projections in separable banach spaces
    • L. Zajíček, "On the points of multivaluedness of metric projections in separable Banach spaces", Comment. Math. Univ. Carolin. 19 (1978), 513-523.
    • (1978) Comment. Math. Univ. Carolin. , vol.19 , pp. 513-523
    • Zajíček, L.1
  • 190
    • 4244056209 scopus 로고
    • On differentiation of metric projections in finite dimensional banach spaces
    • L. Zajíček, "On differentiation of metric projections in finite dimensional Banach spaces", Czech. Math. J. 33 (1983), 325-336.
    • (1983) Czech. Math. J. , vol.33 , pp. 325-336
    • Zajíček, L.1
  • 191
    • 0000223562 scopus 로고
    • Differentiability of the distance function and points of multi-valuedness of the metric projection in banach space
    • L. Zajíček, "Differentiability of the distance function and points of multi-valuedness of the metric projection in Banach space", Czech. Math. J. 33 (1983), 292-308.
    • (1983) Czech. Math. J. , vol.33 , pp. 292-308
    • Zajíček, L.1
  • 192
    • 0039985903 scopus 로고
    • Metric projections and antiprojections in strictly convex normed spaces
    • N. V. Zhivkov, "Metric projections and antiprojections in strictly convex normed spaces", C. R. Acad. Bulgare Sci. 31 (1978), 369-372.
    • (1978) C. R. Acad. Bulgare Sci. , vol.31 , pp. 369-372
    • Zhivkov, N.V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.