Restrictive metric regularity and generalized differential calculus in Banach spaces
We consider nonlinear mappings f:X→Y between Banach spaces and study the notion of restrictive metric regularity of f around some point x¯, that is, metric regularity of f from X into the metric space E=f(X). Some sufficient as well as necessary and sufficient conditions for restrictive metric reg...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204405183 |
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| _version_ | 1832549104012492800 |
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| author | Boris S. Mordukhovich Bingwu Wang |
| author_facet | Boris S. Mordukhovich Bingwu Wang |
| author_sort | Boris S. Mordukhovich |
| collection | DOAJ |
| description | We consider nonlinear mappings f:X→Y
between Banach
spaces and study the notion of restrictive metric
regularity of f
around some point x¯, that is, metric
regularity of f from X into the metric space E=f(X). Some
sufficient as well as necessary and sufficient conditions for
restrictive metric regularity are obtained, which particularly
include an extension of the classical Lyusternik-Graves theorem in
the case when f is strictly differentiable at x¯ but its
strict derivative ∇f(x¯) is not surjective. We develop
applications of the results obtained and some other techniques in
variational analysis to generalized differential calculus
involving normal cones to nonsmooth and nonconvex sets,
coderivatives of set-valued mappings, as well as first-order and
second-order subdifferentials of extended real-valued functions. |
| format | Article |
| id | doaj-art-73b2056252d4417a88fc0eaf1569a541 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-73b2056252d4417a88fc0eaf1569a5412025-02-03T06:12:17ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004502653268010.1155/S0161171204405183Restrictive metric regularity and generalized differential calculus in Banach spacesBoris S. Mordukhovich0Bingwu Wang1Department of Mathematics, Wayne State University, Detroit, MI 48202, USADepartment of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, USAWe consider nonlinear mappings f:X→Y between Banach spaces and study the notion of restrictive metric regularity of f around some point x¯, that is, metric regularity of f from X into the metric space E=f(X). Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves theorem in the case when f is strictly differentiable at x¯ but its strict derivative ∇f(x¯) is not surjective. We develop applications of the results obtained and some other techniques in variational analysis to generalized differential calculus involving normal cones to nonsmooth and nonconvex sets, coderivatives of set-valued mappings, as well as first-order and second-order subdifferentials of extended real-valued functions.http://dx.doi.org/10.1155/S0161171204405183 |
| spellingShingle | Boris S. Mordukhovich Bingwu Wang Restrictive metric regularity and generalized differential calculus in Banach spaces International Journal of Mathematics and Mathematical Sciences |
| title | Restrictive metric regularity and generalized differential calculus in Banach spaces |
| title_full | Restrictive metric regularity and generalized differential calculus in Banach spaces |
| title_fullStr | Restrictive metric regularity and generalized differential calculus in Banach spaces |
| title_full_unstemmed | Restrictive metric regularity and generalized differential calculus in Banach spaces |
| title_short | Restrictive metric regularity and generalized differential calculus in Banach spaces |
| title_sort | restrictive metric regularity and generalized differential calculus in banach spaces |
| url | http://dx.doi.org/10.1155/S0161171204405183 |
| work_keys_str_mv | AT borissmordukhovich restrictivemetricregularityandgeneralizeddifferentialcalculusinbanachspaces AT bingwuwang restrictivemetricregularityandgeneralizeddifferentialcalculusinbanachspaces |