A GENERAL ITERATIVE METHOD OF FIXED POINTS FOR EQUILIBRIUM PROBLEMS AND OPTIMIZATION PROBLEMS

The purpose of this paper is to present a general iterative scheme as below:and to prove that,if {a} and {r} satisfy appropriate conditions,then iteration sequences {x} and{u} converge strongly to a common element of the set of solutions of an equilibrium problem and theset of fixed points of a nonexpansive mapping and the set of solution of a variational inequality,too.Furthermore,by using the above result,we can also obtain an iterative algorithm for solution of anoptimization problem min h(x),where h(x) is a convex and lower semicontinuous functional defined on aclosed convex subset C of a Hilbert space H.The results presented in this paper extend,generalize andimprove the results of Combettes and Hirstoaga,Wittmann,S.Takahashi,Giuseppe Marino,Hong-KunXu,and some others.