Abstract:
We introduce a new model of the system of generalized vector quasi-equilibrium problems with upper semicontinuous set-valued maps and present several existence results of a solution for this system of generalized vector quasi-equilibrium problems and its special cases. The results in this paper extend and improve some results in the literature.

Abstract:
A new mathematical model of generalized vector quasiequilibrium problem with set-valued mappings is introduced, and several existence results of a solution for the generalized vector quasiequilibrium problem with and without -condensing mapping are shown. The results in this paper extend and unify those results in the literature.

Abstract:
本文研究了一类集值广义强向量拟均衡问题组解的存在性问题.利用集值映射的自然拟C-凸性和集值映射的下（-C）-连续性的定义和Kakutani-Fan-Glicksberg不动点定理，在不要求锥C的对偶锥C*具有弱*紧基的情况下，建立了该类集值广义强向量拟均衡问题组解的存在性定理.所得结果推广了该领域的相关结果. In this paper, we study existence of solutions to a system of generalized strong vector quasi-equilibrium problems with set-valued mappings. By making use of definitions of natural quasi C-convexity and lower (-C)-continuity of a set-valued mapping and Kakutani-Fan-Glicksberg fixed point theorem, an existence theorem for solutions to the systems of generalized strong vector quasi-equilibrium problems with set-valued mappings (for short, SSGSVQEP) was established without the assumption that the dual of the ordering cone has a weak* compact base, which extends and improves the corresponding results in this area

Abstract:
Two kinds of parametric set-valued vector quasi-equilibrium problems are introduced. The existence of solutions to these problems is studied. The upper and lower semicontinuities of their solution maps with respect to the parameters are investigated.

Abstract:
In this paper, we introduce a new class of generalized strongly set-valued nonlinear complementarity problems and construct new iterative algorithms. We show the existence of solutions for this kind of nonlinear complementarity problems and the convergence of iterative sequences generated by the algorithm. Our results extend some recent results in this field.

Abstract:
We study the set-valued vector equilibrium problems and the set-valued vector Hartman-Stampacchia variational inequalities. We prove the existence of solutions of the two problems. In addition, we prove the connectedness and the compactness of solutions of the two problems in normed linear space.

Abstract:
We study the set-valued vector equilibrium problems and the set-valued vector Hartman-Stampacchia variational inequalities. We prove the existence of solutions of the two problems. In addition, we prove the connectedness and the compactness of solutions of the two problems in normed linear space.

Abstract:
The purpose of this paper is to prove the strong convergence theorem for finding a common element of the set of fixed point problems of strictly pseudocontractive mapping in Hilbert spaces and two sets of generalized equilibrium problems by using the hybrid method.

Abstract:
This paper is devoted to the characterizations of the boundedness and nonemptiness of solution sets for set-valued vector equilibrium problems in reflexive Banach spaces, when both the mapping and the constraint set are perturbed by different parameters. By using the properties of recession cones, several equivalent characterizations are given for the set-valued vector equilibrium problems to have nonempty and bounded solution sets. As an application, the stability of solution set for the set-valued vector equilibrium problem in a reflexive Banach space is also given. The results presented in this paper generalize and extend some known results in Fan and Zhong (2008), He (2007), and Zhong and Huang (2010).

Abstract:
In this paper, we consider a multiobjective optimal control problem where the preference relation in the objective space is de?ned in terms of a pointed convex cone containing the origin, which de?nes generalized Pareto optimality. For this problem, we introduce the set-valued return function V and provide a unique characterization for V in terms of contingent derivative and coderivative for set-valued maps, which extends two previously introduced notions of generalized solution to the Hamilton-Jacobi equation for single objective optimal control problems.