Implicit Multifunction Theorems in Banach Spaces
This paper is mainly devoted to the study of implicit multifunction theorems in terms of Clarke coderivative in general Banach spaces. We present new sufficient conditions for the local metric regularity, metric regularity, Lipschitz-like property, nonemptiness, and lower semicontinuity of implicit...
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| Vydáno v: | Journal of Applied Mathematics Ročník 2014; číslo 2014; s. 901 - 907-884 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Cairo, Egypt
Hindawi Limiteds
01.01.2014
Hindawi Puplishing Corporation Hindawi Publishing Corporation John Wiley & Sons, Inc Wiley |
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| ISSN: | 1110-757X, 1687-0042 |
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| Abstract | This paper is mainly devoted to the study of implicit multifunction theorems in terms of Clarke coderivative in general Banach spaces. We present new sufficient conditions for the local metric regularity, metric regularity, Lipschitz-like property, nonemptiness, and lower semicontinuity of implicit multifunctions in general Banach spaces. The basic tools of our analysis involve the Ekeland variational principle, the Clarke subdifferential, and the Clarke coderivative. |
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| AbstractList | This paper is mainly devoted to the study of implicit multifunction theorems in terms of Clarke coderivative in general Banach spaces. We present new sufficient conditions for the local metric regularity, metric regularity, Lipschitz-like property, nonemptiness, and lower semicontinuity of implicit multifunctions in general Banach spaces. The basic tools of our analysis involve the Ekeland variational principle, the Clarke subdifferential, and the Clarke coderivative. |
| Audience | Academic |
| Author | Yang, Ming-ge Xu, Yi-fan |
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| Cites_doi | 10.1137/0713043 10.11650/twjm/1500406035 10.1007/BFb0120989 10.1007/BFb0120850 10.1016/j.na.2008.04.005 10.1007/s11590-012-0580-7 10.1016/j.na.2011.06.005 10.11650/twjm/1500405272 10.1016/j.jmaa.2007.05.001 10.1007/s10957-012-0058-x 10.1137/0712056 10.1023/A:1008775413250 10.1016/j.na.2009.12.039 |
| ContentType | Journal Article |
| Contributor | Xu, Yi-fan |
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| Copyright | Copyright © 2014 Ming-ge Yang and Yi-fan Xu. COPYRIGHT 2014 John Wiley & Sons, Inc. Copyright © 2014 Ming-ge Yang and Yi-fan Xu. Ming-ge Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Copyright 2014 Hindawi Publishing Corporation |
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| References_xml | – volume: 72 start-page: 3594 issue: 9-10 year: 2010 end-page: 3601 ident: 11 article-title: Relationships between Robinson metric regularity and Lipschitz-like behavior of implicit multifunctions – reference: Mordukhovich B. S. Variational Analysis and Generalized Differentiation vol I: Basic Theory 2006 Berlin, Germany Springer – volume: 155 start-page: 558 year: 2012 end-page: 571 ident: 15 article-title: Stability of Implicit Multifunctions in Banach Spaces – volume: 74 start-page: 6256 issue: 17 year: 2011 end-page: 6264 ident: 12 article-title: Lipschitz-like property of an implicit multifunction and its applications – volume: 14 start-page: 2107 issue: 5 year: 2010 end-page: 2123 ident: 10 article-title: Metric regularity of parametric generalized inequality systems – volume: 70 start-page: 2806 issue: 7 year: 2009 end-page: 2815 ident: 8 article-title: Point-based sufficient conditions for metric regularity of implicit multifunctions – volume: 8 start-page: 329 issue: 1 year: 2014 end-page: 341 ident: 13 article-title: A note on implicit multifunction theorems – volume: 13 start-page: 497 issue: 4 year: 1976 end-page: 513 ident: 2 article-title: Stability theory for systems of inequalities, II. Differentiable nonlinear systems – reference: Mordukhovich B. S. Variational Analysis and Generalized Differentiation vol II: Applications 2006 Berlin, Germany Springer – reference: Clarke F. H. Optimization and Nonsmooth Analysis 1983 New York, NY, USA Wiley – volume: 19 start-page: 200 year: 1982 end-page: 221 ident: 4 article-title: Generalized equations and their solutions, II. Applications to nonlinear programming – volume: 12 start-page: 195 issue: 1-2 year: 2004 end-page: 223 ident: 6 article-title: Error bounds and implicit multifunction theorem in smooth Banach spaces and applications to optimization – volume: 7 start-page: 209 issue: 3 year: 1999 end-page: 238 ident: 5 article-title: Implicit multifunction theorems – volume: 14 start-page: 497 issue: 3 year: 2013 end-page: 517 ident: 14 article-title: Random implicit function theorems in Asplund spaces with applications – volume: 13 start-page: 47 issue: 1 year: 2009 end-page: 65 ident: 9 article-title: Stability of implicit multifunctions in Asplund spaces – volume: 12 start-page: 754 issue: 5 year: 1975 end-page: 769 ident: 1 article-title: Stability theory for systems of inequalities, I. Linear systems – volume: 10 start-page: 128 year: 1979 end-page: 141 ident: 3 article-title: Generalized equations and their solutions, I. Basic theory – volume: 338 start-page: 11 issue: 1 year: 2008 end-page: 22 ident: 7 article-title: Normal coderivative for multifunctions and implicit function theorems – volume: 13 start-page: 497 issue: 4 year: 1976 ident: 14 publication-title: SIAM Journal on Numerical Analysis doi: 10.1137/0713043 – year: 1983 ident: 3 – volume: 14 start-page: 2107 issue: 5 year: 2010 ident: 6 publication-title: Taiwanese Journal of Mathematics doi: 10.11650/twjm/1500406035 – volume: 19 start-page: 200 year: 1982 ident: 16 publication-title: Mathematical Programming Studies doi: 10.1007/BFb0120989 – ident: 15 doi: 10.1007/BFb0120850 – ident: 18 doi: 10.1016/j.na.2008.04.005 – volume: 8 start-page: 329 issue: 1 year: 2014 ident: 12 publication-title: Optimization Letters doi: 10.1007/s11590-012-0580-7 – ident: 2 doi: 10.1016/j.na.2011.06.005 – volume: 13 start-page: 47 issue: 1 year: 2009 ident: 5 publication-title: Taiwanese Journal of Mathematics doi: 10.11650/twjm/1500405272 – ident: 8 doi: 10.1016/j.jmaa.2007.05.001 – year: 2006 ident: 10 – ident: 4 doi: 10.1007/s10957-012-0058-x – volume: 14 start-page: 497 issue: 3 year: 2013 ident: 17 publication-title: Journal of Nonlinear and Convex Analysis – volume: 12 start-page: 754 issue: 5 year: 1975 ident: 13 publication-title: SIAM Journal on Numerical Analysis doi: 10.1137/0712056 – volume: 7 start-page: 209 issue: 3 year: 1999 ident: 7 publication-title: Set-Valued Analysis doi: 10.1023/A:1008775413250 – ident: 1 doi: 10.1016/j.na.2009.12.039 – volume: 12 start-page: 195 issue: 1-2 year: 2004 ident: 11 publication-title: Set-Valued Analysis – year: 2006 ident: 9 |
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| SubjectTerms | Banach space Banach spaces Economic models Error analysis Functional equations Functions Mathematical analysis Mathematical research Regularity Theorems Variational principles |
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