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Volumn 5, Issue 4, 2001, Pages 323-358

Generalized variation of mappings with applications to composition operators and multifunctions

Author keywords

Bounded variation; Lipschitzian Nemytski composition operators; Metric space valued mappings; Regular selections; Set valued mappings

Indexed keywords


EID: 0041025123     PISSN: 13851292     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011879221347     Document Type: Article
Times cited : (32)

References (51)
  • 1
    • 0003301548 scopus 로고
    • Differential inclusions: Set-valued maps and viability theory
    • Springer-Verlag, Berlin, Heidelberg, New York
    • Aubin, J.-P. and Cellina, A.: Differential Inclusions: Set-Valued Maps and Viability Theory. Grundlehren der math. Wissenschaften Vol. 264, Springer-Verlag, Berlin, Heidelberg, New York, 1984.
    • (1984) Grundlehren der Math. Wissenschaften , vol.264
    • Aubin, J.-P.1    Cellina, A.2
  • 3
    • 0003211244 scopus 로고
    • Convex analysis and measurable multifunctions
    • Springer-Verlag, Berlin
    • Castaing, C. and Valadier, M.: Convex Analysis and Measurable Multifunctions. Lecture Notes in Math. Vol. 580, Springer-Verlag, Berlin, 1977.
    • (1977) Lecture Notes in Math. , vol.580
    • Castaing, C.1    Valadier, M.2
  • 4
    • 0031123969 scopus 로고    scopus 로고
    • On mappings of bounded variation
    • Chistyakov, V.V.: On mappings of bounded variation. J. Dynam. Control Systems 3 (2), 261-289, 1997.
    • (1997) J. Dynam. Control Systems , vol.3 , Issue.2 , pp. 261-289
    • Chistyakov, V.V.1
  • 5
    • 0001299831 scopus 로고    scopus 로고
    • On the theory of set-valued maps of bounded variation of one real variable
    • Chistyakov, V.V.: On the theory of set-valued maps of bounded variation of one real variable. (in Russian) Mat. Sbornik 189 (5), (1998), 153-176. English transl.: Sbornik: Mathematics 189 (5), (1998), 797-819.
    • (1998) Mat. Sbornik , vol.189 , Issue.5 , pp. 153-176
    • Chistyakov, V.V.1
  • 6
    • 0032325980 scopus 로고    scopus 로고
    • Chistyakov, V.V.: On the theory of set-valued maps of bounded variation of one real variable. (in Russian) Mat. Sbornik 189 (5), (1998), 153-176. English transl.: Sbornik: Mathematics 189 (5), (1998), 797-819.
    • (1998) Sbornik: Mathematics , vol.189 , Issue.5 , pp. 797-819
  • 7
    • 52849128915 scopus 로고    scopus 로고
    • Intern. Confer. Dedicated to the 90th Anniversary of L. S. Pontryagin. Abstracts: Optimal Control and Appendices. Moscow State (Lomonosov) University, Moscow
    • Chistyakov, V.V.: Set-valued mappings of bounded variation and their regular selections. Intern. Confer. Dedicated to the 90th Anniversary of L. S. Pontryagin. Abstracts: Optimal Control and Appendices. Moscow State (Lomonosov) University, Moscow, 44-46, 1998.
    • (1998) Set-valued Mappings of Bounded Variation and Their Regular Selections , pp. 44-46
    • Chistyakov, V.V.1
  • 8
    • 85037437376 scopus 로고    scopus 로고
    • Selections of set-valued mappings of bounded Riesz p-variation and their differentiability properties
    • to appear
    • Chistyakov, V.V.: Selections of set-valued mappings of bounded Riesz p-variation and their differentiability properties. (in Russian) Mat. Sbornik (to appear).
    • Mat. Sbornik
    • Chistyakov, V.V.1
  • 10
    • 22044432655 scopus 로고    scopus 로고
    • On maps of bounded p-variation with p > 1
    • Chistyakov, V.V. and Galkin, O.E.: On maps of bounded p-variation with p > 1. Positivity 2 (1), (1998), 19-45.
    • (1998) Positivity , vol.2 , Issue.1 , pp. 19-45
    • Chistyakov, V.V.1    Galkin, O.E.2
  • 11
    • 0032050010 scopus 로고    scopus 로고
    • Mappings of bounded Φ-variation with arbitrary function Φ
    • Chistyakov, V.V. and Galkin, O.E.: Mappings of bounded Φ-variation with arbitrary function Φ. J. Dynam. Control Systems 4 (2), (1998), 217-247.
    • (1998) J. Dynam. Control Systems , vol.4 , Issue.2 , pp. 217-247
    • Chistyakov, V.V.1    Galkin, O.E.2
  • 12
    • 0002211604 scopus 로고
    • Multivalued mappings and Borel sets
    • Čoban, M.M.: Multivalued mappings and Borel sets. (in Russian) Dokl. Akad. Nauk SSSR 182 (1968), 514-517. English transl.: Soviet Math. Dokl. 9, 1968, 1175-1178.
    • (1968) Dokl. Akad. Nauk SSSR , vol.182 , pp. 514-517
    • Čoban, M.M.1
  • 13
    • 0040579104 scopus 로고
    • Čoban, M.M.: Multivalued mappings and Borel sets. (in Russian) Dokl. Akad. Nauk SSSR 182 (1968), 514-517. English transl.: Soviet Math. Dokl. 9, 1968, 1175-1178.
    • (1968) Soviet Math. Dokl. , vol.9 , pp. 1175-1178
  • 16
    • 0000548068 scopus 로고
    • Über lineare funktionaloperationen
    • Helly, E.: Über lineare Funktionaloperationen. S.-B. Akad. Wiss. Wien 121 (1912), 265-297.
    • (1912) S.-B. Akad. Wiss. Wien , vol.121 , pp. 265-297
    • Helly, E.1
  • 17
    • 0000077852 scopus 로고
    • Existence and properties of solutions of ẋ ∈ R(t, x)
    • SIAM Publications
    • Hermes, H.: Existence and properties of solutions of ẋ ∈ R(t, x). Studies in Appl. Math., SIAM Publications (5), (1969), 188-193.
    • (1969) Studies in Appl. Math. , Issue.5 , pp. 188-193
    • Hermes, H.1
  • 18
    • 84968465429 scopus 로고
    • On continuous and measurable selections and the existence of solutions of generalized differential equations
    • Hermes, H.: On continuous and measurable selections and the existence of solutions of generalized differential equations. Proc. Amer. Math. Soc. 29 (3), (1971), 535-542.
    • (1971) Proc. Amer. Math. Soc. , vol.29 , Issue.3 , pp. 535-542
    • Hermes, H.1
  • 19
    • 0001048449 scopus 로고
    • Sur la série de fourier
    • Jordan, C.: Sur la série de Fourier. C. R. Acad. Sci 92 (5), (1881), 228-230.
    • (1881) C. R. Acad. Sci , vol.92 , Issue.5 , pp. 228-230
    • Jordan, C.1
  • 20
    • 0001308809 scopus 로고
    • On the absolute continuity of multifunctions and orientor fields
    • Kikuchi, N. and Tomita, Y.: On the absolute continuity of multifunctions and orientor fields. Funkcial. Ekvac. 14 (3), (1971), 161-170.
    • (1971) Funkcial. Ekvac. , vol.14 , Issue.3 , pp. 161-170
    • Kikuchi, N.1    Tomita, Y.2
  • 21
    • 0041173278 scopus 로고
    • r[a, b]
    • r[a, b]. Fasc. Math. 21 (1990), 79-85.
    • (1990) Fasc. Math. , vol.21 , pp. 79-85
    • Knop, J.1
  • 22
    • 84972544461 scopus 로고
    • Nonlinear semi-groups in Hubert spaces
    • Komura, Y.: Nonlinear semi-groups in Hubert spaces. J. Math. Soc. Japan 19 (1967), 493-507.
    • (1967) J. Math. Soc. Japan , vol.19 , pp. 493-507
    • Komura, Y.1
  • 23
    • 84972508342 scopus 로고
    • Differentiability of nonlinear semigroups
    • Komura, Y.: Differentiability of nonlinear semigroups. J. Math. Soc. Japan 21 (1969), 375-402.
    • (1969) J. Math. Soc. Japan , vol.21 , pp. 375-402
    • Komura, Y.1
  • 26
    • 0004480637 scopus 로고
    • Real and functional analysis
    • Third Edition, Springer-Verlag, New York, Berlin
    • Lang, S.: Real and Functional Analysis. Graduate Texts in Math. Vol. 142, Third Edition, Springer-Verlag, New York, Berlin, 1993.
    • (1993) Graduate Texts in Math. , vol.142
    • Lang, S.1
  • 27
    • 0004151888 scopus 로고
    • Thesis. Technische Hogeschool te Delft, The Netherlands
    • Luxemburg, W.A.J.: Banach function spaces. Thesis. Technische Hogeschool te Delft, The Netherlands, 1955.
    • (1955) Banach Function Spaces
    • Luxemburg, W.A.J.1
  • 28
    • 0011668226 scopus 로고
    • On characterization of Lipschitzian operators of substitution in the class of Hölder functions
    • Matkowska, A.: On characterization of Lipschitzian operators of substitution in the class of Holder functions. Sci. Bull. Łódź Tech. Univ. 17 (1984), 81-85.
    • (1984) Sci. Bull. Łódź Tech. Univ. , vol.17 , pp. 81-85
    • Matkowska, A.1
  • 29
    • 0001557664 scopus 로고
    • Functional equations and Nemytskii operators
    • Matkowski, J.: Functional equations and Nemytskii operators. Funkcial. Ekvac. 25 (2), (1982), 127-132.
    • (1982) Funkcial. Ekvac. , vol.25 , Issue.2 , pp. 127-132
    • Matkowski, J.1
  • 30
    • 0011680039 scopus 로고
    • Form of Lipschitz operators of substitution in Banach spaces of differentiable functions
    • Matkowski, J.: Form of Lipschitz operators of substitution in Banach spaces of differentiable functions. Sci. Bull. Łódź Tech. Univ. 17 (1984), 5-10.
    • (1984) Sci. Bull. Łódź Tech. Univ. , vol.17 , pp. 5-10
    • Matkowski, J.1
  • 31
    • 0002804416 scopus 로고
    • On Nemytskii operator
    • Matkowski, J.: On Nemytskii operator. Math. Japon. 33 (1), (1988), 81-86.
    • (1988) Math. Japon. , vol.33 , Issue.1 , pp. 81-86
    • Matkowski, J.1
  • 33
    • 84985349780 scopus 로고
    • On a characterization of Lipschitzian operators of substitution in the space BV〈a, b〉
    • Matkowski, J. and Miś, J.: On a characterization of Lipschitzian operators of substitution in the space BV〈a, b〉. Math. Nachr. 117 (1984), 155-159.
    • (1984) Math. Nachr. , vol.117 , pp. 155-159
    • Matkowski, J.1    Miś, J.2
  • 34
    • 0041173277 scopus 로고
    • A generalization of a theorem of F. Riesz
    • Medvedev, Yu. T.: A generalization of a theorem of F. Riesz. (in Russian) Uspekhi Mat. Nauk 8 (6), (1953), 115-118.
    • (1953) Uspekhi Mat. Nauk , vol.8 , Issue.6 , pp. 115-118
    • Medvedev, Yu.T.1
  • 35
    • 0001042534 scopus 로고
    • On a characterization of Lipschitzian operators of substitution in the space of bounded Riesz φ-variation
    • Merentes, N.: On a characterization of Lipschitzian operators of substitution in the space of bounded Riesz φ-variation. Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 34 (1991), 139-144.
    • (1991) Ann. Univ. Sci. Budapest. Eötvös Sect. Math. , vol.34 , pp. 139-144
    • Merentes, N.1
  • 36
    • 0039393994 scopus 로고
    • On Nemytskii operator and set-valued functions of bounded p-variation
    • Merentes, N. and Nikodem, K.: On Nemytskii operator and set-valued functions of bounded p-variation. Rad. Mat. 8 (1), (1992), 139-145.
    • (1992) Rad. Mat. , vol.8 , Issue.1 , pp. 139-145
    • Merentes, N.1    Nikodem, K.2
  • 37
    • 0030527159 scopus 로고
    • On characterization of the Lipschitzian composition operator between spaces of functions of bounded p-variation
    • Merentes, N. and Rivas, S.: On characterization of the Lipschitzian composition operator between spaces of functions of bounded p-variation. Czechoslovak Math. J. 45 (4), (1995), 627-637.
    • (1995) Czechoslovak Math. J. , vol.45 , Issue.4 , pp. 627-637
    • Merentes, N.1    Rivas, S.2
  • 38
    • 0001232090 scopus 로고
    • Continuous selections
    • Michael, E. A.: Continuous selections. I. Ann. Math. 63 (2), (1956), 361-382.
    • (1956) I. Ann. Math. , vol.63 , Issue.2 , pp. 361-382
    • Michael, E.A.1
  • 40
    • 84972513402 scopus 로고
    • Multi-valued contraction mappings
    • Nadler, S.B.: Multi-valued contraction mappings. Pacific J. Math. 30 (1969), 475-488.
    • (1969) Pacific J. Math. , vol.30 , pp. 475-488
    • Nadler, S.B.1
  • 42
    • 0039393996 scopus 로고
    • K-convex and K-concave set-valued functions
    • Rozprawy Naukowe
    • Nikodem, K.: K-convex and K-concave set-valued functions. Zeszyty Nauk. Politech. Łódź Mat. 559, Rozprawy Naukowe 114, 1989.
    • (1989) Zeszyty Nauk. Politech. Łódź Mat. , vol.559 , pp. 114
    • Nikodem, K.1
  • 43
    • 84968480766 scopus 로고
    • An embedding theorem for spaces of convex sets
    • Rådström, H.: An embedding theorem for spaces of convex sets. Proc. Amer. Math. Soc. 3 (1), (1952), 165-169.
    • (1952) Proc. Amer. Math. Soc. , vol.3 , Issue.1 , pp. 165-169
    • Rådström, H.1
  • 44
    • 0000732178 scopus 로고
    • Untersuchungen über systeme integrierbarer funktionen
    • Riesz, F.: Untersuchungen über Systeme integrierbarer Funktionen. Math. Ann. 69 (1910), 449-497.
    • (1910) Math. Ann. , vol.69 , pp. 449-497
    • Riesz, F.1
  • 46
    • 0040020149 scopus 로고
    • Jensen equation and Nemytskii operator for set-valued functions
    • Smajdor, A. and Smajdor, W.: Jensen equation and Nemytskii operator for set-valued functions. Rad. Mat. 5 (1989), 311-320.
    • (1989) Rad. Mat. , vol.5 , pp. 311-320
    • Smajdor, A.1    Smajdor, W.2
  • 47
    • 0011664834 scopus 로고
    • Composition of Sobolev functions and application
    • Univ. Los Andes, Venezuela
    • Szigeti, F.: Composition of Sobolev functions and application. Notas de Matemáticas, Univ. Los Andes, Venezuela 86 (1987), 1-25.
    • (1987) Notas de Matemáticas , vol.86 , pp. 1-25
    • Szigeti, F.1
  • 48
    • 0041173276 scopus 로고
    • On Lipschitzian operators of substitution in the space of set-valued functions of bounded variation
    • Zawadzka, G.: On Lipschitzian operators of substitution in the space of set-valued functions of bounded variation. Rad. Mat. 6 (1990), 279-293.
    • (1990) Rad. Mat. , vol.6 , pp. 279-293
    • Zawadzka, G.1
  • 49
    • 0000601081 scopus 로고
    • Single valued representation of absolutely continuous set-valued mappings
    • Zhu Qiji: Single valued representation of absolutely continuous set-valued mappings. Kexue Tongbao 31 (7), (1986), 443-446.
    • (1986) Kexue Tongbao , vol.31 , Issue.7 , pp. 443-446
    • Zhu, Q.1
  • 51
    • 0013097619 scopus 로고
    • On some properties of functions of generalized variation
    • Maligranda, L. and Orlicz, W.: On some properties of functions of generalized variation. Monatsh. Math. 104 (1987), 53-65.
    • (1987) Monatsh. Math. , vol.104 , pp. 53-65
    • Maligranda, L.1    Orlicz, W.2


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