关于修正Ishikawa型迭代的强收敛和一定的控制条件

数学季刊 ›› 2011, Vol. 26 ›› Issue (4): 578-584.

关于修正Ishikawa型迭代的强收敛和一定的控制条件

School of Mathematics, Shandong Institute of Business and Technology

收稿日期:2009-09-04 出版日期:2011-12-30 发布日期:2023-04-14
作者简介: WANG Xue-wu(1963-), male, native of Qinggang, Heilongjiang, an associate professor of Shandong Institute of Business and Technology, engages in probability limit and iterative approximation theory.

Strong Convergence and Certain Control Conditions for Modified Ishikawa Type Iteration

School of Mathematics, Shandong Institute of Business and Technology

Received:2009-09-04 Online:2011-12-30 Published:2023-04-14
About author: WANG Xue-wu(1963-), male, native of Qinggang, Heilongjiang, an associate professor of Shandong Institute of Business and Technology, engages in probability limit and iterative approximation theory.

摘要/Abstract

摘要： In this paper, we establish the strong convergent theorems of an iterative algorithm for asymptotically nonexpansive mappings in Banach spaces and nonexpansive mappings in uniformly smooth Banach spaces, respectively. The results presented in this paper not only give an affirmative partial answer to Reich’s open question, but also generalize and improve the corresponding results of Chang, Lee and Chan [7] and Kim and Xu [10].

关键词: asymptotically nonexpansive mapping, iterative scheme, strong convergence; fixed point

Abstract: In this paper, we establish the strong convergent theorems of an iterative algorithm for asymptotically nonexpansive mappings in Banach spaces and nonexpansive mappings in uniformly smooth Banach spaces, respectively. The results presented in this paper not only give an affirmative partial answer to Reich’s open question, but also generalize and improve the corresponding results of Chang, Lee and Chan [7] and Kim and Xu [10].

Key words: asymptotically nonexpansive mapping, iterative scheme, strong convergence; fixed point

王学武. 关于修正Ishikawa型迭代的强收敛和一定的控制条件[J]. 数学季刊, 2011, 26(4): 578-584.

WANG Xue-wu. Strong Convergence and Certain Control Conditions for Modified Ishikawa Type Iteration[J]. Chinese Quarterly Journal of Mathematics, 2011, 26(4): 578-584.