期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2004
卷号：2004
DOI：10.1155/S0161171204405183
出版社：Hindawi Publishing Corporation
摘要：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.
