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Volumn 5, Issue 1, 1997, Pages 1-35

Submonotone Mappings in Banach Spaces and Applications

Author keywords

Asplund spaces; Differentiability; Minimal w* cusco mappings; Quasi differentiable functions; Subdifferentials; Submonotone mappings

Indexed keywords


EID: 0000901864     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008604928549     Document Type: Article
Times cited : (21)

References (29)
  • 1
    • 0003006591 scopus 로고
    • Minimal cuscos and subgradients of Lipschitz functions
    • M. Thera and J.-B. Bailon (eds), Fixed Point Theory and Its Applications, Longman, Harlow
    • Borwein, J. M.: Minimal cuscos and subgradients of Lipschitz functions, in: M. Thera and J.-B. Bailon (eds), Fixed Point Theory and Its Applications, Pitman Res. Notes in Math. 252, Longman, Harlow, 1991, pp. 57-82.
    • (1991) Pitman Res. Notes in Math. , vol.252 , pp. 57-82
    • Borwein, J.M.1
  • 2
    • 0001468398 scopus 로고
    • The differentiability of real functions on normed linear spaces using generalized subgradients
    • Borwein, J. M., Fitzpatrick, S. P. and Giles, J. R.: The differentiability of real functions on normed linear spaces using generalized subgradients, J. Math. Anal. Appl. 128 (1987), 512-534.
    • (1987) J. Math. Anal. Appl. , vol.128 , pp. 512-534
    • Borwein, J.M.1    Fitzpatrick, S.P.2    Giles, J.R.3
  • 3
    • 84966216580 scopus 로고
    • Theorems of Namioka and R. E. Johnson type for upper semicontinuous and compact valued set-valued mappings
    • Christensen, J. P. R.: Theorems of Namioka and R. E. Johnson type for upper semicontinuous and compact valued set-valued mappings, Proc. Amer. Math. Soc. 86 (1982), 649-655.
    • (1982) Proc. Amer. Math. Soc. , vol.86 , pp. 649-655
    • Christensen, J.P.R.1
  • 4
    • 0042013835 scopus 로고
    • Dense strong continuity of mappings and the Radon-Nikodym property
    • Christensen, J. P. R and Kenderov, P. S.: Dense strong continuity of mappings and the Radon-Nikodym property, Math. Scandinavica 54 (1984), 70-78.
    • (1984) Math. Scandinavica , vol.54 , pp. 70-78
    • Christensen, J.P.R.1    Kenderov, P.S.2
  • 7
    • 84968482238 scopus 로고
    • Generic Frechet differentiability and perturbed optimization problems in Banach spaces
    • Ekeland, I. and Lebourg, G.: Generic Frechet differentiability and perturbed optimization problems in Banach spaces, Trans. Amer. Math. Soc. 224 (1976), 193-216.
    • (1976) Trans. Amer. Math. Soc. , vol.224 , pp. 193-216
    • Ekeland, I.1    Lebourg, G.2
  • 8
    • 0003261417 scopus 로고
    • Geometric Functional Analysis and Its Applications
    • Springer-Verlag, New York
    • Holmes, R.: Geometric Functional Analysis and Its Applications, Graduate Texts in Math. 24, Springer-Verlag, New York, 1975.
    • (1975) Graduate Texts in Math. , vol.24
    • Holmes, R.1
  • 9
    • 0043015625 scopus 로고
    • Locally Lipschitz and regular functions are Frechet differentiable almost everywhere in Asplund spaces
    • Georgiev, P. G.: Locally Lipschitz and regular functions are Frechet differentiable almost everywhere in Asplund spaces, Compt. Rend. Acad. Bulg. Sci. 42(5) (1989), 13-15.
    • (1989) Compt. Rend. Acad. Bulg. Sci. , vol.42 , Issue.5 , pp. 13-15
    • Georgiev, P.G.1
  • 10
    • 0012679725 scopus 로고
    • Submonotone mappings in Banach spaces and differentiability of nonconvex functions
    • Georgiev, P. G.: Submonotone mappings in Banach spaces and differentiability of nonconvex functions, Compt. Rend. Acad. Bulg. Sci. 42(6) (1989), 13-16.
    • (1989) Compt. Rend. Acad. Bulg. Sci. , vol.42 , Issue.6 , pp. 13-16
    • Georgiev, P.G.1
  • 11
    • 0011668785 scopus 로고
    • Convex Analysis with Application in Differentiation of Convex Functions
    • Longman, Boston, London, Melbourne
    • Giles, J. R.: Convex Analysis with Application in Differentiation of Convex Functions, Pitman Res. Notes in Math. 58, Longman, Boston, London, Melbourne, 1982.
    • (1982) Pitman Res. Notes in Math. , vol.58
    • Giles, J.R.1
  • 12
    • 0043015624 scopus 로고
    • The quasi-differentiable functionals are almost everywhere differentiable
    • Bulg. Acad. Sci., Sofia
    • Kenderov, P. S.: The quasi-differentiable functionals are almost everywhere differentiable, in: Math, and Education Math., Proc. 2nd Spring Conf. Bulg. Math. Soc., Bulg. Acad. Sci., Sofia, 1973, pp. 123-126.
    • (1973) Math, and Education Math., Proc. 2nd Spring Conf. Bulg. Math. Soc. , pp. 123-126
    • Kenderov, P.S.1
  • 14
    • 0010896371 scopus 로고
    • Monotone operators in Asplund spaces
    • Kenderov, P. S.: Monotone operators in Asplund spaces, Compt. Rend. Acad. Bulg. Sci. 30 (1977), 963-965.
    • (1977) Compt. Rend. Acad. Bulg. Sci. , vol.30 , pp. 963-965
    • Kenderov, P.S.1
  • 15
    • 84972507805 scopus 로고
    • Dense strong continuity of pointwise continuous mappings
    • Kenderov, P. S.: Dense strong continuity of pointwise continuous mappings, Pacific J. Math. 89 (1980), 111-130.
    • (1980) Pacific J. Math. , vol.89 , pp. 111-130
    • Kenderov, P.S.1
  • 16
    • 0042013833 scopus 로고
    • Continuity-like properties of set-valued mappings
    • Kenderov, P. S.: Continuity-like properties of set-valued mappings, Serdica Bulg. Math. Publ. 9 (1983), 149-160.
    • (1983) Serdica Bulg. Math. Publ. , vol.9 , pp. 149-160
    • Kenderov, P.S.1
  • 17
    • 24444442819 scopus 로고
    • Noveaux resultatas generiques sur les operateurs monotones dans les espaces de Banach
    • Kenderov, P. S. and Robert, R.: Noveaux resultatas generiques sur les operateurs monotones dans les espaces de Banach, CR Acad. Sci. Paris 282 (1976), S. A-845-847.
    • (1976) CR Acad. Sci. Paris , vol.282
    • Kenderov, P.S.1    Robert2    R3
  • 18
    • 84968486313 scopus 로고
    • Generic differentiability of Lipschitzian functions
    • Lebourg, G.: Generic differentiability of Lipschitzian functions, Trans. Amer. Math. Soc. 256 (1979), 125-144.
    • (1979) Trans. Amer. Math. Soc. , vol.256 , pp. 125-144
    • Lebourg, G.1
  • 19
    • 0000012763 scopus 로고
    • Semismooth and semiconvex functions in constrained optimization
    • Mifflin, R.: Semismooth and semiconvex functions in constrained optimization, SIAM J. Control Optim. 15 (1977), 959-972.
    • (1977) SIAM J. Control Optim. , vol.15 , pp. 959-972
    • Mifflin, R.1
  • 20
    • 84972488065 scopus 로고
    • Monotone (nonlinear) operators in Hilbert space
    • Minty, J. R.: Monotone (nonlinear) operators in Hilbert space, Duke Math. J. 29 (1962), 341-344.
    • (1962) Duke Math. J. , vol.29 , pp. 341-344
    • Minty, J.R.1
  • 21
    • 0003466110 scopus 로고
    • Convex Functions, Monotone Operators and Differentiability, 2nd edn, Springer-Verlag, Berlin
    • Phelps, R. R.: Convex Functions, Monotone Operators and Differentiability, 2nd edn, Lect. Notes in Math. 1364, Springer-Verlag, Berlin, 1993.
    • (1993) Lect. Notes in Math. , vol.1364
    • Phelps, R.R.1
  • 22
    • 51249177342 scopus 로고
    • Smooth Banach spaces, weak Asplund spaces and monotone or usco mappings
    • Preiss, D., Phelps, R. R. and Namioka, I.: Smooth Banach spaces, weak Asplund spaces and monotone or usco mappings, Israel J. Math. 72 (1990), 257-279.
    • (1990) Israel J. Math. , vol.72 , pp. 257-279
    • Preiss, D.1    Phelps, R.R.2    Namioka, I.3
  • 24
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, NJ
    • Rockafellar, R. T.: Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 25
    • 0001091630 scopus 로고
    • Local boundedness of nonlinear monotone operators
    • Rockafellar, R. T.: Local boundedness of nonlinear monotone operators, Michigan Math. J. 16 (1969), 397-407.
    • (1969) Michigan Math. J. , vol.16 , pp. 397-407
    • Rockafellar, R.T.1
  • 26
    • 84968466806 scopus 로고
    • Submonotone subdifferentials of Lipschitz functions
    • Spingarn, J. E.: Submonotone subdifferentials of Lipschitz functions, Trans. Amer. Math. Soc. 264 (1981), 77-89.
    • (1981) Trans. Amer. Math. Soc. , vol.264 , pp. 77-89
    • Spingarn, J.E.1
  • 27
    • 0010891381 scopus 로고
    • A generalization of an Ekeland-Lebourg theorem and the differentiability of distance functions
    • Zajicek, L.: A generalization of an Ekeland-Lebourg theorem and the differentiability of distance functions, Supl. Rend. del Circolo Mat. Palermo, II 3 (1984), 403-410.
    • (1984) Supl. Rend. del Circolo Mat. Palermo, II , vol.3 , pp. 403-410
    • Zajicek, L.1
  • 28
    • 0000223562 scopus 로고
    • Differentiability of the distance function and points of multivaluedness of the metric projection in Banach space
    • Zajicek, L.: Differentiability of the distance function and points of multivaluedness of the metric projection in Banach space, Czechoslovak Math. J. 33 (1983), 292-308.
    • (1983) Czechoslovak Math. J. , vol.33 , pp. 292-308
    • Zajicek, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.