Iteration $x_{n 1}=\alpha_{n 1}f(x_n) (1-\alpha_{n 1})T_{n 1}x_n$ for an Infinite Family of Nonexpansive Maps $\{T_n\}_{n=1}^\infty$
Received:May 07, 2007  Revised:March 08, 2008
Key Words: infinitely many nonexpansive mappings   contractive mapping   weakly sequential continuity.  
Fund Project:the Youth Founction of Sichuan Educational committee (No.08ZB002); the Foundation of Yibin College (No.2006Q01).
Author NameAffiliation
RAO Ruo Feng Department of Mathematics, Yibin College, Sichuan 644007, China 
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Abstract:
      Under the framework of uniformly smooth Banach spaces, Chang$^{[1]}$ proved in 2006 that the sequence $\{x_n\}$ generated by the iteration $x_{n 1}= \alpha_{n 1}f(x_n) (1-\alpha_{n 1})T_{n 1}x_n$ converges strongly to a common fixed point of a finite family of nonexpansive maps $\{T_n\}$, where $f: C\to C$ is a contraction. However, in this paper, the author considers the iteration in more general case that $\{T_n\}$ is an infinite family of nonexpansive maps, and proves that Chang's result holds still in the setting of reflexive Banach spaces with the weakly sequentially continuous duality mapping.
Citation:
DOI:10.3770/j.issn:1000-341X.2009.04.009
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