Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013, Special Issue (2013), Article ID 539061, 11 pages.
Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces
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.
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 539061, 11 pages.
First available in Project Euclid: 26 February 2014
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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