System of Operator Quasi Equilibrium Problems

We consider a system of operator quasi equilibrium problems and system of generalized quasi operator equilibrium problems in topological vector spaces. Using a maximal element theorem for a family of set-valued mappings as basic tool, we derive some existence theorems for solutions to these problems with and without involving Φ-condensing mappings.

The Equilibrium Existence Theorem for Systems of General Quasiequilibrium Problems in GFC-Spaces

In this paper, the GFC-KKM mapping is introduced and a GFC-KKM theorem is established in GFC-spaces. As applications, a matching theorem and a maximal element theorem are obtained. Our results unify, improve and generalize some known results in recent reference. Finally, an equilibrium existence theorem for systems of general quasiequilibrium problems is yielded in GFC-spaces.

A Maximal Element Theorem inFWC-Spaces and Its Applications

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem inFWC-spaces. The results represented in this paper unify and extend some known results in the literature.

A New Maximal Theorem in Product GFC-Spaces with Application to Systems of Generalized Mixed Vector Quasiequilibrium Problems

In this paper, a new maximal element theorem is established in product GFC-spaces. As application, a new existence theorem of solutions for systems of generalized mixed vector quasi-equilibrium problems is obtained.

Existence Results for Nonsmooth Vector Quasi-Variational-Like Inequalities

We introduce nonsmooth vector quasi-variational-like inequalities (NVQVLI) by means of a bifunction. We establish some existence results for solutions of these inequalities by using Fan-KKM theorem and a maximal element theorem. By using the technique and methodology adopted in Al-Homidan et al. (2012), one can easily derive the relations among these inequalities and a vector quasi-optimization problem. Hence, the existence results for a solution of a vector quasi-optimization problem can be derived by using our results. The results of this paper extend several known results in the literature.

Approximate fixed points on almost convex sets

In this paper, we deduce a maximal element theorem on multimaps and an approximate fixed point theorem on almost convex sets. This generalizes the well-known Himmelberg fixed point theorem and also unifies recent results of Park and Tan [14] %cite{tan2} and Sy and Park [16].