Restrictive metric regularity in variational analysis Original Research Article

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→Yf:X→Y with the range restricted to the image f(X)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.