SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.

GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMSIN LOCALLY G-CONVEX SPACES

Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces.. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.

Continuity of the Solution Mappings for Parametric Generalized Strong Vector Equilibrium Problems

The stability analysis of the solution mappings for vector equilibrium problems is an important topic in optimization theory and its applications. In this paper, we focus on the continuity of the solution mapping for a parametric generalized strong vector equilibrium problem. By virtue of a nonlinear scalarization technique, a new density result of the solution mapping is obtained. Based on the density result, we give sufficient conditions for the lower semicontinuity and the Hausdorff upper semicontinuity of the solution mapping to the parametric generalized strong vector equilibrium problem. In addition, some examples were given to illustrate that our results improve ones in the literature.

Upper and Lower Semicontinuity of Solution Sets for Parametric Generalized Vector Quasi-equilibrium Problems

In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated.

NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.

NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.

LEVITIN-POYAK WELL-POSEDNESS OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS WITH FUNCTIONAL CONSTRAINTS

In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are given.

QUASI-EQUILIBRIUM PROBLEMS AND CONSTRAINED MULTIOBJECTIVE GAMES IN GENERALIZED CONVEX SPACE

A class of quasi-equilibrium problems and a class of constrained multiobjective games were introduced and studied in generalized convex spaces without linear structure. First, two existence theorems of solutions for quasi-equilibrium problems are proved in noncompact generalized convex spaces. Then, ar applications of the quasi-equilibrium existence theorem, several existence theorems of weighted Nash-equilibria and Pareto equilibria for the constrained multiobjective games are established in noncompact generalized convex spaces. These theorems improve, unify, and generalize the corresponding results of the multiobjective games in recent literatures.

GENERIC STABILITY AND EXISTENCE OF ESSENTIAL COMPONENTS OF THE SOLUTION SET FOR THE SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS

By using Fort theorem the generic stability result for the system of generalized vector equilibrium problems is established. Further, by proving the existence and connectivity of minimal essential set the existence result of essential components in the solution set is derived.

Strong Convergence of an Iterative Method for Generalized Mixed Equilibrium Problems and Fixed Point Problems

In this paper, we introduce a hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of nonexpansive mappings. Furthermore, we show a strong convergence theorem under some mild conditions.

QUASI_EQUILIBRIUM PROBLEMS IN NONCOMPACT GENERALIZED CONVEX SPACES

By applying a new fixed point theorem due to the author, some new equilibrium existence theorems of quasi-equilibrium problems are proved in noncompact generalized convex spaces. These theorems improve and generalize a number of important known results in recent literature.

MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES

In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.

Existence results for generalized vector equilibrium problems with applications

By a coincidence theorem, some existence theorems of solutions are proved for four types of generalized vector equilibrium problems with moving cones. Applications to the generalized semi-infinite programs with the generalized vector equilibrium constraints under the mild conditions are also given. The results of this paper unify and improve the corresponding results in the previous literature.

SYSTEM OF VECTOR QUASI-EQUILIBRIUM PROBLEMS AND ITS APPLICATIONS

A new system of vector quasi-equilibrium problems is introduced and its existence of solution is proved. As applications, some existence results of weak Pareto equilibrium for both constrained multicriteria games and multicriteria games without constrained correspondences are also shown.

PREDICTOR-CORRECTOR ALGORITHMS FOR SOLVING GENERALIZED MIXED IMPLICIT QUASI-EQUILIBRIUM PROBLEMS

A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal （resp., proper, Pareto, weak） quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.

An Iterative Algorithm for Generalized Mixed Equilibrium Problems and Fixed Points of Nonexpansive Semigroups

In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.

Generalized mixed equilibrium problem in Banach spaces

This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-C- nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study the optimization problem. It shows that our results improve and extend the corresponding results announced by many others recently.

QUASI-VARIATIONAL INEQUALITIES AND SOCIAL EQUILIBRIUM

A quasi-variational inequality is proved in paracompact setting which generalizes the results of Zhou Chen andAubin. As applications, two existence theorems on the solutions of optimization problems and social equilibria ofmetagames are showed which improve and extend the recent results of Kaczynski-Zeidan and Aubin.

A Penalty Approach for Generalized Nash Equilibrium Problem

The generalized Nash equilibrium problem （GNEP） is a generalization of the standard Nash equilibrium problem （NEP）, in which both the utility function and the strategy space of each player depend on the strategies chosen by all other players. This problem has been used to model various problems in applications. However, the convergent solution algorithms are extremely scare in the literature. In this paper, we present an incremental penalty method for the GNEP, and show that a solution of the GNEP can be found by solving a sequence of smooth NEPs. We then apply the semismooth Newton method with Armijo line search to solve latter problems and provide some results of numerical experiments to illustrate the proposed approach.