Iterative Methods To The Common Elements Of Equilibrium Problems And The Set Of Fixed Points

In this paper, we deal with some convergence theorems of iterative methods to the common elements of equilibrium problems and the set of fixed points problems. In the first chapter, we introduce some revelent definitions, important lemmas and recent results for the equilibrium problems and the set of fixed points problems.In the second chapter, we introduce a new convergence theorem for finding the common solutions of an equilibrium problem and the set of solutions of the varia-tional inequality and fixed point of finite hemi-relatively non-expansive mappings in use of hybrid proximal-point methods in uniformly smooth and uniformly convex Ba-nach space.In the third chapter, We establish a new hybrid iterative scheme for finding the common solutions of a generalized equilibrium problem, the set of solutions of the vari-ational inequality and the fixed point of monotone mappings and finite hemi-relatively non-expansive mappings in uniformly smooth and 2-uniformly convex Banach space by which we get a strong convergence theorem.In the fourth chapter, we establish a new viscosity extragradient approximation method to investigate the problem of finding the common element of the set of com-mon fixed points of infinite family of strict pseudo-contractions mappings, the set of generalized equilibrium problems and the set of solutions to a system of variational inequalities in Hilbert Space.