Implicit multifunction theorems in complete metric spaces

In this paper, we establish some new characterizations of metric regularity of implicit multifunctions in complete metric spaces by using lower semicontinuous envelopes of the distance functions to set-valued mappings. Through these new characterizations it is possible to investigate implicit multif...

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Vydané v:	Mathematical programming Ročník 139; číslo 1-2; s. 301 - 326
Hlavní autori:	Huynh, van Ngai, Nguyen, Huu Tron, Théra, Michel
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer-Verlag 01.06.2013 Springer Nature B.V Springer Verlag
Predmet:	Analysis Banach spaces Calculus of Variations and Optimal Control; Optimization Combinatorics Computer science Derivatives Full Length Paper Functions (mathematics) Inequality Mathematical analysis Mathematical and Computational Physics Mathematical functions Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Metric space Numerical Analysis Perturbation methods Regularity Stability Studies Theorems Theoretical Generalized equations Perturbation stability 90C30 49J53 49J52 Error bound Implicit multifunction Metric regularity
ISSN:	0025-5610, 1436-4646
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Abstract	In this paper, we establish some new characterizations of metric regularity of implicit multifunctions in complete metric spaces by using lower semicontinuous envelopes of the distance functions to set-valued mappings. Through these new characterizations it is possible to investigate implicit multifunction theorems based on coderivatives and on contingent derivatives as well as the perturbation stability of implicit multifunctions.
AbstractList	Issue Title: Special Issue: Computational and Analytical Mathematics In this paper, we establish some new characterizations of metric regularity of implicit multifunctions in complete metric spaces by using lower semicontinuous envelopes of the distance functions to set-valued mappings. Through these new characterizations it is possible to investigate implicit multifunction theorems based on coderivatives and on contingent derivatives as well as the perturbation stability of implicit multifunctions.[PUBLICATION ABSTRACT] In this paper, we establish some new characterizations of metric regularity of implicit multifunctions in complete metric spaces by using lower semicontinuous envelopes of the distance functions to set-valued mappings. Through these new characterizations it is possible to investigate implicit multifunction theorems based on coderivatives and on contingent derivatives as well as the perturbation stability of implicit multifunctions.
Author	Huynh, van Ngai Théra, Michel Nguyen, Huu Tron
Author_xml	– sequence: 1 givenname: van Ngai surname: Huynh fullname: Huynh, van Ngai organization: Department of Mathematics, University of Quy Nhon – sequence: 2 givenname: Huu Tron surname: Nguyen fullname: Nguyen, Huu Tron organization: Department of Mathematics, University of Quy Nhon – sequence: 3 givenname: Michel surname: Théra fullname: Théra, Michel email: michel.thera@unilim.fr organization: Laboratoire XLIM, UMR-CNRS 7252, Université de Limoges
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Snippet	In this paper, we establish some new characterizations of metric regularity of implicit multifunctions in complete metric spaces by using lower semicontinuous... Issue Title: Special Issue: Computational and Analytical Mathematics In this paper, we establish some new characterizations of metric regularity of implicit...
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SubjectTerms	Analysis Banach spaces Calculus of Variations and Optimal Control; Optimization Combinatorics Computer science Derivatives Full Length Paper Functions (mathematics) Inequality Mathematical analysis Mathematical and Computational Physics Mathematical functions Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Metric space Numerical Analysis Perturbation methods Regularity Stability Studies Theorems Theoretical
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Title	Implicit multifunction theorems in complete metric spaces
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