Coincidence and fixed point theorems with applications

Abstract

In this paper, we first establish a coincidence theorem under the noncompact settings. Then we derive some fixed point theorems for a family of functions. We apply our fixed point theorem to study nonempty intersection problems for sets with convex sections and obtain a social equilibrium existence theorem. We also introduce a concept of a quasi-variational inequalities and prove an existence result for a solution to such a system.