## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2012, Special Issue (2012), Article ID 474031, 15 pages.

### Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in $q$-Uniformly Smooth and Strictly Convex Banach Spaces

#### Abstract

We introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in $q$-uniformly smooth and strictly convex Banach spaces. We also proved the strong convergence theorems of implicit and explicit schemes. The results obtained in this paper extend and improve many recent ones announced by many others.

#### Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 474031, 15 pages.

Dates
First available in Project Euclid: 3 January 2013

https://projecteuclid.org/euclid.jam/1357179976

Digital Object Identifier
doi:10.1155/2012/474031

Mathematical Reviews number (MathSciNet)
MR2959975

Zentralblatt MATH identifier
1325.47134

#### Citation

Wen, Meng; Hu, Changsong; Wu, Zhiyu. Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in $q$ -Uniformly Smooth and Strictly Convex Banach Spaces. J. Appl. Math. 2012, Special Issue (2012), Article ID 474031, 15 pages. doi:10.1155/2012/474031. https://projecteuclid.org/euclid.jam/1357179976

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