\(V\)-prox-regular functions in smooth Banach spaces (Q2220509)

Summary: 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.