## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2014), Article ID 809528, 6 pages.

### Strong Convergence Theorems for Common Fixed Points of an Infinite Family of Asymptotically Nonexpansive Mappings

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#### Abstract

In the framework of a real Banach space with uniformly Gateaux differentiable norm, some new viscosity iterative sequences $\{{x}_{n}\}$ are introduced for an infinite family of asymptotically nonexpansive mappings ${\left\{{T}_{i}\right\}}_{i=1}^{\infty}$ in this paper. Under some appropriate conditions, we prove that the iterative sequences $\{{x}_{n}\}$ converge strongly to a common fixed point of the mappings ${\left\{{T}_{i}\right\}}_{i=1}^{\infty}$, which is also a solution of a variational inequality. Our results extend and improve some recent results of other authors.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 809528, 6 pages.

**Dates**

First available in Project Euclid: 6 October 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1412606022

**Digital Object Identifier**

doi:10.1155/2014/809528

**Mathematical Reviews number (MathSciNet)**

MR3226233

**Zentralblatt MATH identifier**

07023120

#### Citation

Wang, Yuanheng. Strong Convergence Theorems for Common Fixed Points of an Infinite Family of Asymptotically Nonexpansive Mappings. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 809528, 6 pages. doi:10.1155/2014/809528. https://projecteuclid.org/euclid.aaa/1412606022

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