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Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings

Fixed Point Theory and Applications volume 2008, Article number: 732193 (2008) Cite this article

Abstract

Using the implicit iteration and the hybrid method in mathematical programming, we prove weak and strong convergence theorems for finding common fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Our results include many convergence theorems by Xu and Ori (2001) and Zhang and Su (2007) as special cases. We also apply our method to find a common element to the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem. Finally, we propose an iteration to obtain convergence theorems for a continuous monotone mapping.

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Authors and Affiliations

  1. Department of Mathematics, Khon Kaen University, Khon Kaen, 40002, Thailand

    Kittikorn Nakprasit & Satit Saejung

  2. Department of Mathematics, Statistics and Computer, Ubon Rajathanee University, Ubon Ratchathani, 34190, Thailand

    Weerayuth Nilsrakoo

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  1. Kittikorn Nakprasit
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  2. Weerayuth Nilsrakoo
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  3. Satit Saejung
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Correspondence to Satit Saejung.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Nakprasit, K., Nilsrakoo, W. & Saejung, S. Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings. Fixed Point Theory Appl 2008, 732193 (2008). https://doi.org/10.1155/2008/732193

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  • DOI: https://doi.org/10.1155/2008/732193

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