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

• Main Authors: Chin-Tzong Pang, Eskandar Naraghirad
• Format: Article
• Language: English
• Published: Hindawi Limited 2013-01-01
• Series: Abstract and Applied Analysis
• Online Access: http://dx.doi.org/10.1155/2013/539061

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.