[1]吴莉.Banach空间中渐近非扩张映射的收敛定理[J].东南大学学报(自然科学版),2003,33(6):804-806.[doi:10.3969/j.issn.1001-0505.2003.06.029]
 Wu Li.Convergence theorems for asymptotically nonexpansive mappings in Banach space[J].Journal of Southeast University (Natural Science Edition),2003,33(6):804-806.[doi:10.3969/j.issn.1001-0505.2003.06.029]
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Banach空间中渐近非扩张映射的收敛定理()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
33
期数:
2003年第6期
页码:
804-806
栏目:
数学、物理学、力学
出版日期:
2003-11-20

文章信息/Info

Title:
Convergence theorems for asymptotically nonexpansive mappings in Banach space
作者:
吴莉12
1 南京工程学院基础部, 南京 210036; 2 南京大学数学系, 南京 210093
Author(s):
Wu Li12
1 Department of Basic Courses, Nanjing Institute of Technology, Nanjing 210036, China
2 Department of Mathematics, Nanjing University, Nanjing 210093, China
关键词:
渐近非扩张映射 一致凸Banach空间 Opial条件
Keywords:
asymptotically nonexpansive mapping uniformly convex Banach space Opial’s condition
分类号:
O177.91
DOI:
10.3969/j.issn.1001-0505.2003.06.029
摘要:
X为具有Opial条件的一致凸Banach空间,CX的非空有界闭凸子集, T, SC到自身的2个渐近非扩张映射且TS有公共的不动点. 本文主要考察了一种带误差的迭代逼近TS有公共的不动点, 在迭代参数{an}, {bn}, {cn}, {a’n}, {
Abstract:
Let X be a uniform Banach space satisfying Opial condition and C a nonempty bounded closed convex subset of X. Let T, S be two asymptotically nonexpansive mappings on C with F(T)∩F(S)≠. This paper deals with approximating common fixed point of T and S through an iterative sequence with errors. Under some suitable assumptions on the iteration parameters {an}, {bn}, {cn}, {a’n}, {b’n}, and {c’n}, we have proved that the iterative sequence with errors converges weakly to some common fixed point of T and S. We also investigate the strong convergence of such iterative sequence.

参考文献/References:

[1] Das G,Debata J P.Fixed points of quasi-nonexpansive mappings [J].Indian J Pure Appl Math,1986,17(4):1263-1269.
[2] Takshashi W,Tamura T.Convergence theorems for a pair of nonexpansive mappings [J].J Convex Analysis, 1995,5(1):45-48.
[3] Khan S H,Takahashi W.Approximating common fixed points of two asymptotically nonexpansive mappings [J]. Scie Math Jap,2001,53(1):133-138.
[4] Chu J.Weak and strong convergence to fixed points of asymptotically nonexpansive mappings[J]. Bull Austral Math Soc,1991,43(1):153-159.
[5] Tan K K,Xu H K.Approximating fixed points of nonexpansive mappings by Ishikawa iteration [J]. Proce J Anal Appl,1993,178(2):301-308.
[6] Grornichi J.Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach space [J].Comment Math Univ Carolin,1989,30(1):249-252.

备注/Memo

备注/Memo:
作者简介: 吴莉(1975—),女,硕士生,讲师,wuli75@vip.sina.com.
更新日期/Last Update: 2003-11-20