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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204405183 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |