期刊名称：Advances in Mathematical Finance and Applications
印刷版ISSN：2538-5569
电子版ISSN：2645-4610
出版年度：2022
卷号：7
期号：2
页码：391-404
DOI：10.22034/amfa.2021.1935453.1617
语种：English
出版社：Islamic Azad University of Arak
摘要：In this paper, first a brief history of equilibrium problems(EP) and generalized implicit vector equilibrium problems(GIVEP) are given. Then some existence theorems for GIVEP are presented, also some suitable conditions in order the solution set of GIVEP is compact and convex for set-valued mappings whose are a subset of the cartesian product of Hausdorff topological vector space and their range is a subset of a topological space values (not necessarily locally convex or a topological vector space). In almost all of published results for GIVEP the set-valued mappings are considered from a topological vector space(locally convex topological vector space) to a topological vector space while in this paper the range of the set-valued mappings are a subsets of a topological spaces. As applications of our results, we derive some suitable conditions for existing a normalized Nash equilibrium problems when the number of players are finite and the abstract case, that is infinite players. Finally, a numerical result, as an application of the main results, is given. The method used for proving the existence theorems is based on finite intersection theorems and Ky-Fan’s theorem. The results of this paper, can be considered as suitable generalizations of the published paper in this area.
