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Journal of Inequalities and Applications
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A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings

Journal of Inequalities and Applications volume 2009, Article number: 520301 (2009) Cite this article

Abstract

A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for the inverse-strongly monotone mapping which solves some variational inequalities. Moreover, we apply our main result to obtain strong convergence to a common fixed point of nonexpansive mapping and strictly pseudocontractive mapping in a Hilbert space.

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  1. Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand

    Chakkrid Klin-eam & Suthep Suantai

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  1. Chakkrid Klin-eam
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  2. Suthep Suantai
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Correspondence to Suthep Suantai.

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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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Klin-eam, C., Suantai, S. A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings. J Inequal Appl 2009, 520301 (2009). https://doi.org/10.1155/2009/520301

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  • DOI: https://doi.org/10.1155/2009/520301

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