Common Fixed Point Theorems on Weakly Contractive and Nonexpansive Mappings

被引:0
作者
Jian-Zhong Xiao
Xing-Hua Zhu
机构
[1] Nanjing University of Information Science and Technology,Department of Mathematics
来源
Fixed Point Theory and Applications | / 2008卷
关键词
Banach Space; Error Estimate; Convex Subset; Convergence Theorem; Nonexpansive Mapping;
D O I
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中图分类号
学科分类号
摘要
A family of commuting nonexpansive self-mappings, one of which is weakly contractive, are studied. Some convergence theorems are established for the iterations of types Krasnoselski-Mann, Kirk, and Ishikawa to approximate a common fixed point. The error estimates of these iterations are also given.
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共 17 条
[1]  
Alber YI(2001)On the projection methods for fixed point problems Analysis 21 17-39
[2]  
Guerre-Delabriere S(1998)The principle of weakly contractive mappings in metric spaces Communications on Applied Nonlinear Analysis 5 45-68
[3]  
Alber YI(2001)Some theorems on weakly contractive maps Nonlinear Analysis: Theory, Methods and Applications 47 2683-2693
[4]  
Guerre-Delabriere S(2003)Common fixed-point results in best approximation theory Applied Mathematics Letters 16 575-580
[5]  
Zelenko L(1996)The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space Journal of Mathematical Analysis and Applications 202 150-159
[6]  
Rhoades BE(1992)Krasnoselski-Mann iterations in normed spaces Canadian Mathematical Bulletin 35 21-28
[7]  
Hussain N(1971)On successive approximations for nonexpansive mappings in Banach spaces Glasgow Mathematical Journal 12 6-9
[8]  
Khan AR(1974)Fixed points by a new iteration method Proceedings of the American Mathematical Society 44 147-150
[9]  
Bauschke HH(1976)Fixed points and iteration of a nonexpansive mapping in a Banach space Proceedings of the American Mathematical Society 59 65-71
[10]  
Borwein J(1993)Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process Journal of Mathematical Analysis and Applications 178 301-308