Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces

Implicit Mann process and Halpern-type iteration have been extensively studied by many others. In this paper, in order to find a common fixed point of a countable family of nonexpansive mappings in the framework of Banach spaces, we propose a new implicit iterative algorithm related to a strongly ac...

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Bibliographic Details
Main Authors: Ming Tian, Xin Jin
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/264910
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Summary:Implicit Mann process and Halpern-type iteration have been extensively studied by many others. In this paper, in order to find a common fixed point of a countable family of nonexpansive mappings in the framework of Banach spaces, we propose a new implicit iterative algorithm related to a strongly accretive and Lipschitzian continuous operator F:xn=αnγV(xn)+βnxn-1+((1-βn)I-αnμF)Tnxn and get strong convergence under some mild assumptions. Our results improve and extend the corresponding conclusions announced by many others.
ISSN:1085-3375
1687-0409