The Preliminary Study Of Solving Equilibrium Problems' Algorithms

This thesis deals with the following problem (EP): finding x~*∈X, such that f(x~*, y)≥0,(?)y∈X. Where X is a given set, f : X×X→R is a bifunction.The equilibrium problems contains as special cases for instance optimization problem, problems of Nash Equilibrium, complementarity problems, fixed point problems and varational inequalities. It also can be employed to study the engineering, the management science and the mathmatical economics. This thesis strives to study some methods of solving equilibrium problems. We obtain some strong convergence theorems which improve and extend recent results. This thesis consists of four chapters. They are managed as follows:In the first chapter, we curtly introduce the equilibrium problem and its researching status.In the second chaper, we study an Ishikawa iterative to find a common element of the set of solutions of an equilibrium problem and the set of fixed points problem and we can get a strong convergence theorem.In the third chaper, we introduce an extra-gradient algorithm to solve a common element of the set of solutions of an equilibrium problem and the fixed point problems. And then we prove the strong convergency of the the sequences generated by the iterative processes.In the fourth chapter, we give a new iterative algorithm to solve the eqilibrium problems, the fixed point problems and the variational inclusion problems. And we obtain a prove the convergence theorem.