On Projected Solutions for Quasi Equilibrium Problems with Non-self Constraint Map

Abstract

In a normed space setting, this paper studies the conditions under which the projected solutions to a quasi equilibrium problem with non-self constraint map exist. Our approach is based on an iterative algorithm which gives rise to a sequence such that, under the assumption of asymptotic regularity, its limit points are projected solutions. Finally, as a particular case, we discuss the existence of projected solutions to a quasi variational inequality problem.