Solutions of system of generalized vector quasi-equilibrium problems in locally G-convex uniform spaces

Abstract

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.

The rise and fall of L-spaces

“…Here we found another people who can not distinguish pairs and triples. (9) In 2004, Ding and Xia [18] and Ding, Yao, and Lin [19]: "The notion of a generalized convex (or G-convex) space was introduced under an extra isotonic condition by Park and Kim [48]. Recently Park [35] gave the following definition of a G-convex space by removing the extra condition.…”

Connectedness and Path-Connectedness of Solution Sets to Symmetric Vector Equilibrium Problems

“…The system of vector equilibrium problems, i.e., a family of equilibrium problems for vector-valued bifunctions defined on a product set were introduced by Ansari et al [3] with applications in vector optimization problems and Nash equilibrium problem for vector-valued functions. The system of vector equilibrium problems contain system of equilibrium problems, systems of vector variational inequalities, system of vector variational-like inequalities, system of optimization problems, fixed point problems and several related topics as special cases (see, for example, [3,4,5,15,16,28,30,31,29,34] and the references therein).…”

On the existence of solutions of generalized equilibrium problems with α−β−η -monotone mappings

“…In 2013, Mahato and Nahak published a paper in which they obtained the existence results for mixed equilibrium problems in a reflexive Banach space [12]. Ding and his colleagues considered a collectively fixed point theorem and an equilibrium existence theorem for generalized games in product locally G-convex uniform spaces [8]. However, in recent years, the iterative algorithms of solutions for generalized equilibrium problems have been studied by several authors.…”