Abstract and Applied Analysis

Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces

Chin-Tzong Pang and Eskandar Naraghirad

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Abstract

We introduce a general algorithm to approximate common fixed points for a countable family of nonexpansive mappings in a real Banach space. We prove strong convergence theorems for the sequences produced by the methods and approximate a common fixed point of a countable family of nonexpansive mappings which solves uniquely the corresponding variational inequality. Furthermore, we apply our results for finding a zero of an accretive operator. It is important to state clearly that the contribution of this paper in relation with the previous works (Marino and Xu, 2006) is a technical method to prove strong convergence theorems of a general iterative algorithm for an infinite family of nonexpansive mappings in Banach spaces. Our results improve and generalize many known results in the current literature.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 539061, 11 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393442138

Digital Object Identifier
doi:10.1155/2013/539061

Mathematical Reviews number (MathSciNet)
MR3121491

Zentralblatt MATH identifier
1364.47036

Citation

Pang, Chin-Tzong; Naraghirad, Eskandar. Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 539061, 11 pages. doi:10.1155/2013/539061. https://projecteuclid.org/euclid.aaa/1393442138


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