Projected solutions of generalized quasivariational problems in Banach spaces

Abstract

This paper focuses on the analysis of generalized quasivariational inequalities with non-self map. In Aussel et al., (2016), introduced the concept of the projected solution to study such problems. Subsequently, in the literature, this concept has attracted great attention and has been developed from different perspectives. The main contribution of this paper is to prove new existence results of the projected solution for generalized quasivariational inequality problems with non-self map in suitable infinite dimensional spaces. As an application, a quasiconvex quasioptimization problem is studied through a normal cone approach.