Existence Results for New Weak and Strong Mixed Vector Equilibrium Problems on Noncompact Domain

We introduce and consider two new mixed vector equilibrium problems, that is, a new weak mixed vector equilibrium problem and a new strong mixed vector equilibrium problem which are combinations of certain vector equilibrium problems, and vector variational inequality problems. We prove existence results for the problems in noncompact setting.

Noncompact Equilibrium Points for Set-Valued Maps

We prove a generalized result on the existence of equilibria for a monotone set-valued map defined on noncompact domain and take its values in an order of topological vector space. As consequence, we give a new variational inequality.

Extended Mixed Vector Equilibrium Problems

We study extended mixed vector equilibrium problems, namely, extended weak mixed vector equilibrium problem and extended strong mixed vector equilibrium problem in Hausdorff topological vector spaces. Using generalized KKM-Fan theorem (Ben-El-Mechaiekh et al.; 2005), some existence results for both problems are proved in noncompact domain.

Ekeland Variational Principle for Generalized Vector Equilibrium Problems with Equivalences and Applications

The aim of this paper is to introduce Ekeland variational principle with variants for generalized vector equilibrium problems and to establish some existence results of solutions of generalized vector equilibrium problems with compact or noncompact domain as applications. Finally, some equivalent results of the established Ekeland variational principle are presented.

Noncompact Equilibrium Points and Applications

We prove an equilibrium existence result for vector functions defined on noncompact domain and we give some applications in optimization and Nash equilibrium in noncooperative game.