Abstract and Applied Analysis

Mixed Approximation for Nonexpansive Mappings in Banach Spaces

Qing-Bang Zhang, Fu-Quan Xia, and Ming-Jie Liu

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Abstract

The mixed viscosity approximation is proposed for finding fixed points of nonexpansive mappings, and the strong convergence of the scheme to a fixed point of the nonexpansive mapping is proved in a real Banach space with uniformly Gâteaux differentiable norm. The theorem about Halpern type approximation for nonexpansive mappings is shown also. Our theorems extend and improve the correspondingly results shown recently.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 763207, 12 pages.

Dates
First available in Project Euclid: 2 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1267538589

Digital Object Identifier
doi:10.1155/2010/763207

Mathematical Reviews number (MathSciNet)
MR2587613

Zentralblatt MATH identifier
1195.47045

Citation

Zhang, Qing-Bang; Xia, Fu-Quan; Liu, Ming-Jie. Mixed Approximation for Nonexpansive Mappings in Banach Spaces. Abstr. Appl. Anal. 2010 (2010), Article ID 763207, 12 pages. doi:10.1155/2010/763207. https://projecteuclid.org/euclid.aaa/1267538589


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