Coincidence theorems and its applications to equilibrium problems

Abstract

Given two maps h : X × K → R and g : X → K such that, for all x ∈ X, h(x, g(x)) = 0, we consider the equilibrium problem of findingx ∈ X such that h(x, g(x)) ≥ 0 for every x ∈ X. This question is related to a coincidence problem.Mathematics Subject Classification (2010). Primary 49J40; Secondary 55M20.