$V$-Prox-Regular Functions in Smooth Banach Spaces

Abstract

In this paper, we continue the study of the V -prox-regularity that we have started recently for sets. We define an appropriate concept of the V -prox-regularity for functions in reflexive smooth Banach spaces by adapting the one given in Hilbert spaces. Our main goal is to study the relationship between the V -prox-regularity of a given l.s.c. f and the V -prox-regularity of its epigraph.