## 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

Chin-Tzong Pang and Eskandar Naraghirad

**Full-text: Open access**

#### 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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