Different approaches to the existence of projected solutions in Banach spaces

Abstract

Quasi-equilibrium problems generalize equilibrium problems, as introduced in the framework of Blum and Oettli. This study focuses on quasi-equilibrium problems in which the constraint map is not a self-map. We present various reformulations that establish existence results for projected solutions in Banach spaces. Furthermore, we apply these findings to quasi-variational inequalities and quasi-optimization problems.