Boris S. Mordukhovich, Bingwu Wang, "Restrictive metric regularity and generalized differential calculus in Banach spaces", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 683907, 28 pages, 2004. https://doi.org/10.1155/S0161171204405183
Restrictive metric regularity and generalized differential calculus in Banach spaces
We consider nonlinear mappings between Banach spaces and study the notion of restrictive metric regularity of around some point , that is, metric regularity of from into the metric space . 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 is strictly differentiable at but its strict derivative 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.
Copyright © 2004 Hindawi Publishing Corporation. 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.