The generalized [formula omitted]-projection operator and set-valued variational inequalities in Banach spaces

Abstract

In this paper, we further study some properties of the generalized f -projection operator introduced by Wu and Huang. By employing the properties of the generalized f -projection operator and the well-known KKM and Kakutani–Fan–Glicksberg theorems, we establish some new existence theorems of solutions for two classes of generalized set-valued variational and quasi-variational inequalities in reflexive and smooth Banach spaces under some suitable conditions.