On some generalized multi-valued variational inequalities

Abstract

In this paper, we have introduced a particular kind of generalized quasi-variational inequality and have proved an existence theorem for its solution in reflexive Banach spaces under assumption of h-pseudo-monotonicity and h-hemi-continuity. A fixed-point theorem of h-pseudo-monotone mapping is also proved, which is a further generalization of such result obtained earlier by Singh, Tarafdar, and Watson 22.