Abstract and Applied Analysis

The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces

Rabian Wangkeeree

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Abstract

We introduce two general hybrid iterative approximation methods (one implicit and one explicit) for finding a fixed point of a nonexpansive mapping which solving the variational inequality generated by two strongly positive bounded linear operators. Strong convergence theorems of the proposed iterative methods are obtained in a reflexive Banach space which admits a weakly continuous duality mapping. The results presented in this paper improve and extend the corresponding results announced by Marino and Xu (2006), Wangkeeree et al. (in press), and Ceng et al. (2009).

Article information

Source
Abstr. Appl. Anal., Volume 2011 (2011), Article ID 854360, 19 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313171131

Digital Object Identifier
doi:10.1155/2011/854360

Mathematical Reviews number (MathSciNet)
MR2784383

Zentralblatt MATH identifier
1215.47097

Citation

Wangkeeree, Rabian. The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces. Abstr. Appl. Anal. 2011 (2011), Article ID 854360, 19 pages. doi:10.1155/2011/854360. https://projecteuclid.org/euclid.aaa/1313171131


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