Abstract:
A sufficient condition for the existence of a solution for generalized vector equilibrium problem (GVEP) on Hadamard manifold, by using a version of KKM lemma on this context, is presented in this paper. It is worth to point out that, in particular, existence result of solution for optimization problems, vector optimization problems, Nash equilibria problems, complementarity problems and variational inequality problems can be obtained as a special case of the existence result for GVEP in this new context.

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:
We first define upper sign continuity for a set-valued mappingand then we consider two types of generalized vector equilibrium problems in topologicalvector spaces and provide sufficient conditions under which the solution sets are nonemptyand compact. Finally, we give an application of our main results. The paper generalizesand improves results obtained by Fang and Huang in (2005).

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:
A class of implicit multivalued vector equilibrium problems is studied. By using the generalized Fan-Browder fixed point theorem, some existence results of solutions for the implicit multivalued vector equilibrium problems are obtained under some suitable assumptions. Moreover, a stability result of solutions for the implicit multivalued vector equilibrium problems is derived. These results extend and unify some recent results for implicit vector equilibrium problems, multivalued vector variational inequality problems, and vector variational inequality problems.

Abstract:
We discuss three classes of generalized implicit vector equilibrium problems in topological ordered spaces. Under some conditions, we prove three new existence theorems of solutions for the generalized implicit vector equilibrium problems in topological ordered spaces by using the Fan-Browder fixed point theorem.

Abstract:
We discuss three classes of generalized implicit vector equilibrium problems in topological ordered spaces. Under some conditions, we prove three new existence theorems of solutions for the generalized implicit vector equilibrium problems in topological ordered spaces by using the Fan-Browder fixed point theorem.

Abstract:
In this paper, we firstly prove the existence of the equilibrium for the generalized abstract economy. We apply these results to show the existence of solutions for systems of vector quasi-equilibrium problems with multivalued trifunctions. Secondly, we consider the generalized strong vector quasi-equilibrium problems and study the existence of their solutions in the case when the correspondences are weakly naturally quasi-concave or weakly biconvex and also in the case of weak-continuity assumptions. In all situations, fixed-point theorems are used.

Abstract:
Let and be real Banach spaces, a nonempty closed convex subset of , and a multifunction such that for each is a proper, closed and convex cone with , where denotes the interior of . Given the mappings , , and , we study the generalized vector equilibrium-like problem: find such that for all for some . By using the KKM technique and the well-known Nadler result, we prove some existence theorems of solutions for this class of generalized vector equilibrium-like problems. Furthermore, these existence theorems can be applied to derive some existence results of solutions for the generalized vector variational-like inequalities. It is worth pointing out that there are no assumptions of pseudomonotonicity in our existence results.

Abstract:
We study some properties for parametric generalized vector equilibrium problems and the convergent behavior for the correspondent solution sets of this problem under some suitable conditions. Several existence results and the topological structures of the efficient solutions set are established. Some new results of existence for weak solutions and strong solutions are derived. Finally, we give some examples to illustrate our theory including the example studied by Fang (1992), who established the perturbed nonlinear program and described successfully that the optimal solution of will approach the optimal solution of linear program (P). 1. Introduction and Preliminaries In recent years, the topological structures of the set of efficient solutions for vector equilibrium problems or generalized systems or variational inequality problems have been discussed in several aspects, as we show in [1–29]. More precisely, we divide this subject into several topics as following. First, the closedness of the set of efficient solutions are studied in [1, 4, 6, 13–16, 27]. Second, the lower semicontinuity of the set of efficient solutions are studied in [1, 9, 10, 19, 21, 23–26, 30]. Third, the upper semicontinuity of the set of efficient solutions are studied in [1, 4, 7, 8, 16, 21, 23–26, 30]. Fourth, the connectedness of the set of efficient solutions are studied in [2, 3, 17, 20, 27, 29]. Fifth, the existence of efficient solutions are studied in [5, 6, 8–12, 16–18, 22, 27, 29, 31]. Gong and Yao [19] establish the lower semicontinuity of the set of efficient solutions for parametric generalized systems with monotone bifunctions in real locally convex Hausdorff topological vector spaces. They also discuss the connectedness of the efficient solutions for generalized systems, we refer to [20]. Luc [27, Chapter 6] investigates the structures of efficient point sets of linear, convex, and quasiconvex problems and also points out that the closedness and connectedness of the efficient solutions sets are important in mathematical programming. Huang et al. [8] discuss a class of parametric implicit vector equilibrium problems in Hausdorff topological vector spaces, where the mappings and are perturbed by parameters, say and , respectively. They establish the upper semicontinuity and lower semicontinuity of the solution mapping for such problems and derive the closedness of the set of efficient solutions. Li et al. [1] discuss the generalized vector quasivariational inequality problem and obtain both upper semicontinuous and lower semicontinuous properties of the set of