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2013 Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces
Ming Tian, Xin Jin
Abstr. Appl. Anal. 2013(SI60): 1-9 (2013). DOI: 10.1155/2013/264910

Abstract

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 : x n = α n γ V ( x n ) + β n x n - 1 + ( ( 1 - β n ) I - α n μ F ) T n x n and get strong convergence under some mild assumptions. Our results improve and extend the corresponding conclusions announced by many others.

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Ming Tian. Xin Jin. "Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces." Abstr. Appl. Anal. 2013 (SI60) 1 - 9, 2013. https://doi.org/10.1155/2013/264910

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 06209236
MathSciNet: MR3044993
Digital Object Identifier: 10.1155/2013/264910

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI60 • 2013
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