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

作　　者：Fang ZHANG·Yongfu SUDepartment of Mathematics,Tianjin Polytechnic University,Tianjin 300160,China. 

出　　处：《Journal of Systems Science & Complexity》2009年第3期503-517,共15页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant No. 10771050.

摘　　要：The purpose of this paper is to present a general iterative scheme as below：{F（un,y）＋1/rn（y-un,un-xn）≥0,y∈C,xn＋1=（I-αnA）Sun＋αnγf（xn）and to prove that, if {an} and {rn} satisfy appropriate conditions, then iteration sequences {xn} and {un} 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 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 others.

关 键 词：Eprilibriurn problem nonexpansive mappings optimization problem strong convergence variational inequality. 

分 类 号：O177.91[理学—数学]