Coincidence theorems and its applications to equilibrium problems

Abstract

Given two maps \({h : X \times K \rightarrow \mathbb{R}}\) and g : X → K such that, for all \({x \in X, h(x, g(x)) = 0}\) , we consider the equilibrium problem of finding \({\tilde{x} \in X}\) such that \({h(\tilde{x}, g(x)) \geq 0}\) for every \({x \in X}\) . This question is related to a coincidence problem.