Some New Algorithms For A System Of Equilibrium Problems

The equilibrium problems contains Nash Equilibrium, complementarity problems, fixed point problems and varational inequalities. It also can be employed to study the engineer-ing, the management science and the mathmatical economics. For these reasons, the equilibrium problems has been widely used academic research.In this paper, we discusses the following equilibrium problem (EP):finding x∈C, such that (?)k∈Γ,(?)y∈C,Fk(x,y)≥0,{Fk}k∈Γ:C×Câ†'R. R is a real number set. In this paper, we introduce some parallel and cyclic algorithms for finding a common element of the set to solutions of a system equilibrium problems, the set of the common fixed points of a family of finite strict pseudo-contractions and the solution set of a variational inequality for anα-inverse strongly monotone mapping. We obtain some weak and strong convergence theorems for the sequences generated by these processes in Hilbert spaces. The results in this paper generalize, improve and unify some well-known results in the literature.The first chapter, we introduce the academic significance and the case of the research of a system equilibrium problems.The second chapter,we describe some basic knowledge of a system equilibrium problems.The third chapter,we obtain two strong convergence theorems and two weak convergence theorems which is generated by the new algorithm,and give a strict proof.