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: [GRAPHICS] and to prove that, if {alpha(n)} and {r(n)} satisfy appropriate conditions, then iteration sequences {x(n)} and {u(n)} converge strongly to a common element of the set of solutions of an equilibrium problem and the set 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 an optimization problem min h(x), where h(x) is a convex and lower semicontinuous functional defined on a closed convex subset C (x is an element of C)of a Hilbert space H. The results presented in this paper extend, generalize and improve the results of Combettes and Hirstoaga, Wittmann, S. Takahashi, Giuseppe Marino, Hong-Kun Xu, and some other.