THREE-STEP ITERATIONS FOR NONEXPANSIVE MAPPINGS AND INVERSE-STRONGLY MONOTONE MAPPINGS  

作　　者：Meijuan SHANG Yongfu SU Xiaolong QIN 

机构地区：[1]Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China [2]Department of Mathematics, Shijiazhuang University, Shijiazhuang 050035, China [3]Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China. [4]Department of Mathematics and the Research Institute of Natural Sciences, Gyeongsang National University,Chinju 660-701, Korea.

出　　处：《Journal of Systems Science & Complexity》2009年第2期333-344,共12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：This paper introduces a three-step iteration for finding a common element of the set of fixedpoints of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping by viscosity approximation methods in a Hilbert space.The authors showthat the iterative sequence converges strongly to a common element of the two sets,which solves somevariational inequality.Subsequently,the authors consider the problem of finding a common fixed pointof a nonexpansive mapping and a strictly pseudo-contractive mapping and the problem of finding acommon element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping.The results obtained in this paper extend and improve the correspondingresults announced by Nakajo,Takahashi,and Toyoda.

关 键 词：Inverse-strongly monotone mapping metric projection nonexpansive mapping variational inequality. 

分 类 号：O177.91[理学—数学] O178[理学—基础数学]