Abstract
In this paper, we continue the study of the properties of the generalised projection on nonconvex sets in reflexive smooth Banach spaces with smooth dual norm started by the first author in [9]. We define a new class of nonconvex sets in Banach spaces containing the convex closed sets and having various important properties whenever the space is assumed to be uniformly convex with smooth norm. (C) 2019 Published by Elsevier Inc.