Restrictive metric regularity in variational analysis

Metric regularity is an important property of mappings, which is closely related to the celebrated open mapping theorem and Lyusternik-Graves theorem in nonlinear analysis. The paper is devoted to new developments involving this property and its modifications with applications to modern variational analysis. We introduce a new notion of “restrictive metric regularity”, which is the metric regularity of mappings f:X→Y with the range restricted to the image f(X) of X under f. Some characterizations of this property are given with their applications to the first- and second-order generalized differential calculus in arbitrary Banach spaces.