Iterative Schemes for a Family of Finite Asymptotically Pseudocontractive Mappings in Banach Spaces

作     者：GU Feng GU Feng

作者机构：Institute of Applied Mathematics Hangzhou Normal University Zhejiang 310036 China Department of Mathematics Hangzhou Normal University Zhejiang 310036 China 

出 版 物：《Journal of Mathematical Research and Exposition》 (数学研究与评论（英文版）)

年 卷 期：2009年第29卷第5期

页      面：864-870页

学科分类：0303[法学-社会学] 12[管理学] 1204[管理学-公共管理] 03[法学] 07[理学] 070104[理学-应用数学] 030301[法学-社会学] 0701[理学-数学] 

基　　金：Foundation item: the National Natural Science Foundation of China (No. 10771141) the Natural Science Foundation of Zhejiang Province (Y605191) the Natural Science Foundation of Heilongjiang Province (No. A0211) and the Scientific Research Foundation from Zhejiang Province Education Committee (No. 20051897) 

主　　题：approximated fixed point sequence uniformly asymptotically regular mapping asymptotically pseudocontractive mapping. 

摘      要：Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E. Let Ti ： K→ K, i=1, 2,... ,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε^（i）n} and asymptotically pseudocontractive mappings with sequences {κ^（i）n}, where {κ^（i）n} and {ε^（i）n}, i = 1, 2,... ,N, satisfy certain mild conditions. Let a sequence {xn} be generated from x1 ∈ K by zn：= （1-μn）xn＋μnT^nnxn, xn＋1 ：= λnθnx1＋ [1 - λn（1 ＋ θn）]xn ＋ λnT^nnzn for all integer n ≥ 1, where Tn = Tn（mod N）, and {λn}, {θn} and {μn} are three real sequences in [0, 1] satisfying appropriate conditions. Then ｜｜xn- Tixn｜｜→ 0 as n→∞ for each l ∈ {1, 2,..., N}. The results presented in this paper generalize and improve the corresponding results of Chidume and Zegeye, Reinermann, Rhoades and Schu.