Continuous Selections for Multivalued Mappings with Closed Convex Images and Applications
Some existence theorems of continuous selections for multivalued mappings with closed convex images are proved. As some simple applications, we give some results on fixed points and differential inclusions. The results presented in this paper generalize some recent results.
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Published in | Journal of mathematical analysis and applications Vol. 252; no. 1; pp. 402 - 409 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
San Diego, CA
Elsevier Inc
01.12.2000
Elsevier |
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Abstract | Some existence theorems of continuous selections for multivalued mappings with closed convex images are proved. As some simple applications, we give some results on fixed points and differential inclusions. The results presented in this paper generalize some recent results. |
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AbstractList | Some existence theorems of continuous selections for multivalued mappings with closed convex images are proved. As some simple applications, we give some results on fixed points and differential inclusions. The results presented in this paper generalize some recent results. |
Author | Huang, Fa-lun Li, Hong-xu |
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Keywords | continuous selection differential inclusion fixed point multivalued mapping r-lower semicontinuous partial lower semicontinuous closed convex set Convex set Compact space Topological space Selection Functional analysis Topology Banach space Application Semicontinuous |
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References | Michael (RF1) 1956; 63 Semenov (RF9) 1996; 80 Deimling (RF5) 1985 Deutsch, Kenderov (RF2) 1983; 14 Aubin, Cellina (RF4) 1984 Gutev (RF6) 1993; 50 De Blasi, Myjak (RF3) 1985; 93 Przeslawski, Rybiński (RF7) 1992; 68 Repovs̆, Semenov (RF8) 1994; 49 Pasicki (RF10) 1997; 45 Repovs̆ (10.1006/jmaa.2000.7086_RF8) 1994; 49 Michael (10.1006/jmaa.2000.7086_RF1) 1956; 63 De Blasi (10.1006/jmaa.2000.7086_RF3) 1985; 93 Aubin (10.1006/jmaa.2000.7086_RF4) 1984 Pasicki (10.1006/jmaa.2000.7086_RF10) 1997; 45 Deutsch (10.1006/jmaa.2000.7086_RF2) 1983; 14 Gutev (10.1006/jmaa.2000.7086_RF6) 1993; 50 Deimling (10.1006/jmaa.2000.7086_RF5) 1985 Semenov (10.1006/jmaa.2000.7086_RF9) 1996; 80 Przeslawski (10.1006/jmaa.2000.7086_RF7) 1992; 68 |
References_xml | – volume: 68 start-page: 262 year: 1992 end-page: 282 ident: RF7 article-title: Concepts of lower semicontinuity and continuous selections for convex valued multifunctions publication-title: J. Approx. Theory contributor: fullname: Rybiński – year: 1984 ident: RF4 publication-title: Differential Inclusions contributor: fullname: Cellina – year: 1985 ident: RF5 publication-title: Nonlinear Functional Analysis contributor: fullname: Deimling – volume: 63 start-page: 361 year: 1956 end-page: 382 ident: RF1 article-title: Continuous selection, I publication-title: Ann. of Math. contributor: fullname: Michael – volume: 80 start-page: 2130 year: 1996 end-page: 2139 ident: RF9 article-title: Paraconvexity of graphs of Lipschitzian functions publication-title: J. Math. Sci. contributor: fullname: Semenov – volume: 93 start-page: 369 year: 1985 end-page: 372 ident: RF3 article-title: Continuous selections for weakly Hausdorff lower semicontinuous multifunctions publication-title: Proc. Amer. Math. Soc. contributor: fullname: Myjak – volume: 14 start-page: 185 year: 1983 end-page: 194 ident: RF2 article-title: Continuous selections and approximate selections for set-valued mappings and applications to metric projections publication-title: SIAM J. Math. Anal. contributor: fullname: Kenderov – volume: 50 start-page: 129 year: 1993 end-page: 138 ident: RF6 article-title: Selection theorems under an assumption weaker than lower semicontinuity publication-title: Topology Appl. contributor: fullname: Gutev – volume: 49 start-page: 151 year: 1994 end-page: 190 ident: RF8 article-title: E. Michael's theory of continuous selections: Development and applications publication-title: Uspekhi Mat. Nauk contributor: fullname: Semenov – volume: 45 start-page: 81 year: 1997 end-page: 88 ident: RF10 article-title: Multivalues selections publication-title: Bull. Polish Acad. Sci. Math. contributor: fullname: Pasicki – volume: 93 start-page: 369 year: 1985 ident: 10.1006/jmaa.2000.7086_RF3 article-title: Continuous selections for weakly Hausdorff lower semicontinuous multifunctions publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-1985-0770557-1 contributor: fullname: De Blasi – volume: 63 start-page: 361 year: 1956 ident: 10.1006/jmaa.2000.7086_RF1 article-title: Continuous selection, I publication-title: Ann. of Math. doi: 10.2307/1969615 contributor: fullname: Michael – year: 1985 ident: 10.1006/jmaa.2000.7086_RF5 contributor: fullname: Deimling – volume: 45 start-page: 81 year: 1997 ident: 10.1006/jmaa.2000.7086_RF10 article-title: Multivalues selections publication-title: Bull. Polish Acad. Sci. Math. contributor: fullname: Pasicki – volume: 68 start-page: 262 year: 1992 ident: 10.1006/jmaa.2000.7086_RF7 article-title: Concepts of lower semicontinuity and continuous selections for convex valued multifunctions publication-title: J. Approx. Theory doi: 10.1016/0021-9045(92)90105-W contributor: fullname: Przeslawski – volume: 50 start-page: 129 year: 1993 ident: 10.1006/jmaa.2000.7086_RF6 article-title: Selection theorems under an assumption weaker than lower semicontinuity publication-title: Topology Appl. doi: 10.1016/0166-8641(93)90017-8 contributor: fullname: Gutev – volume: 80 start-page: 2130 year: 1996 ident: 10.1006/jmaa.2000.7086_RF9 article-title: Paraconvexity of graphs of Lipschitzian functions publication-title: J. Math. Sci. doi: 10.1007/BF02362519 contributor: fullname: Semenov – year: 1984 ident: 10.1006/jmaa.2000.7086_RF4 contributor: fullname: Aubin – volume: 49 start-page: 151 year: 1994 ident: 10.1006/jmaa.2000.7086_RF8 article-title: E. Michael's theory of continuous selections: Development and applications publication-title: Uspekhi Mat. Nauk contributor: fullname: Repovs̆ – volume: 14 start-page: 185 year: 1983 ident: 10.1006/jmaa.2000.7086_RF2 article-title: Continuous selections and approximate selections for set-valued mappings and applications to metric projections publication-title: SIAM J. Math. Anal. doi: 10.1137/0514015 contributor: fullname: Deutsch |
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SubjectTerms | closed convex set continuous selection differential inclusion Exact sciences and technology fixed point Functional analysis General topology Mathematical analysis Mathematics multivalued mapping partial lower semicontinuous r-lower semicontinuous Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
Title | Continuous Selections for Multivalued Mappings with Closed Convex Images and Applications |
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Volume | 252 |
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