## Abstract and Applied Analysis

### Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings

Jong Soo Jung

#### Abstract

We propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain different control conditions for viscosity iterative scheme are given and strong convergence of viscosity iterative scheme to a solution of a ceratin variational inequality is established.

#### Article information

Source
Abstr. Appl. Anal., Volume 2009 (2009), Article ID 573156, 17 pages.

Dates
First available in Project Euclid: 16 March 2010

https://projecteuclid.org/euclid.aaa/1268745558

Digital Object Identifier
doi:10.1155/2009/573156

Mathematical Reviews number (MathSciNet)
MR2516000

Zentralblatt MATH identifier
1168.47053

#### Citation

Jung, Jong Soo. Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings. Abstr. Appl. Anal. 2009 (2009), Article ID 573156, 17 pages. doi:10.1155/2009/573156. https://projecteuclid.org/euclid.aaa/1268745558

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