In this paper, we want to solve the Fredholm integral equations of the second type using thenumerical finite differences method. In this method, we use the forward, central and backwardoperator’s to solve integral equations, and finally we compare these methods with the help of nu-merical examples. Manuscript profile

In this paper, first a short history of the notion of equilibrium problem in Economics and Nash$\acute{'}$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonotonicity for vector valued bifunctions is introduced. By using it some existence results for the vector equilibrium problem, in the setting of topological vector spaces, are presented. Some examples in order to illustrate the main results and compare them with the corresponding published results are furnished. Further, the compactness of the solution set of vector equilibrium problem is investigated. Manuscript profile

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. Manuscript profile