Scalarization and Optimality Conditions of E-Globally Proper Efficient Solution for Set-Valued Equilibrium Problems

Abstract

In this paper, our purpose is to use the improvement set to investigate the scalarization and optimality conditions of [Formula: see text]-globally proper efficient solution for the set-valued equilibrium problems with constraints. First, the notion of [Formula: see text]-globally proper efficient solution for set-valued equilibrium problems with constraints is introduced in locally convex Hausdorff topological spaces. Second, the linear scalarization theorems of [Formula: see text]-globally proper efficient solution are derived. Finally, under the assumption of nearly [Formula: see text]-subconvexlikeness, the Kuhn–Tucker and Lagrange optimality conditions for set-valued equilibrium problems with constraints are obtained in the sense of [Formula: see text]-globally proper efficiency. Meanwhile, we give some examples to illustrate our results. The results obtained in this paper improve and generalize some known results in the literature.