Approximate Benson efficient solutions for set-valued equilibrium problems

Abstract

Abstract In locally convex Hausdorff topological vector spaces, the approximate Benson efficient solution is proposed for set-valued equilibrium problems and its relationship to the Benson efficient solution is discussed. Under the assumption of generalized convexity, by using a separation theorem for convex sets, Kuhn–Tucker-type and Lagrange-type optimality conditions for set-valued equilibrium problems are established, respectively.

Keywords

• Approximate Benson efficient solution
• Near cone-subconvexlikeness
• Optimality condition
• Set-valued equilibrium problem