Approximating common fixed points of asymptotically nonexpansive maps in uniformly convex Banach spaces

被引:31
作者
Fukhar-ud-din, Hafiz
Khan, Abdul Rahim [1 ]
机构
[1] King Fahd Univ Petr & Minerals, Dept Math Sci, Dhahran 31261, Saudi Arabia
[2] Islamia Univ, Bahawalpur 63100, Pakistan
关键词
nonexpansive map; common fixed point; three-step iteration process with errors; Opial property; Frechet differentiable norm; Kadec-Klee property; weak convergence; strong convergence; STRONG-CONVERGENCE; WEAK-CONVERGENCE; ITERATION PROCESS; MAPPINGS; THEOREMS; ERRORS;
D O I
10.1016/j.camwa.2007.01.008
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We introduce three-step iterative schemes with errors for two and three nonexpansive maps and establish weak and strong convergence theorems for these schemes. Mann-type and Ishikawa-type convergence results are included in the analysis of these new iteration schemes. The results presented in this paper substantially improve and extend the results due to [S.H. Khan, H. Fukhar-ud-din, Weak and strong convergence of a scheme with errors for two nonexpansive mappings, Nonlinear Anal. 8 (2005) 1295-1301], [N. Shahzad, Approximating fixed points of non-self nonexpansive mappings in Banach spaces, Nonlinear Anal. 61 (2005) 1031-1039], [W. Takahashi, T. Tamura, Convergence theorems for a pair of nonexpansive mappings, J. Convex Anal. 5 (1995) 45-58], [K.K. Tan, H.K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993) 301-308] and [H.F. Senter, W.G. Dotson, Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44 (1974) 375-380]. (c) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1349 / 1360
页数:12
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