Generalized monotone bifunctions and equilibrium problems

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Abstract

Using quasimonotone and pseudomonotone bifunctions, we derive existence results for the following equilibrium problem: given a closed and convex subsetK of a real topological vector space, find \(\bar x \in K\) such that \(F(\bar x,y) \geqslant 0\) for allyK. In addtion, we study the solution set and the uniquencess of a solution. The paper generalizes results obtained recently for variational inequalities.