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On the Existence and Convergence of Approximate Solutions for Equilibrium Problems in Banach Spaces

Journal of Inequalities and Applications volume 2007, Article number: 017294 (2007) Cite this article

Abstract

We introduce and study a new class of auxiliary problems for solving the equilibrium problem in Banach spaces. Not only the existence of approximate solutions of the equilibrium problem is proven, but also the strong convergence of approximate solutions to an exact solution of the equilibrium problem is shown. Furthermore, we give some iterative schemes for solving some generalized mixed variational-like inequalities to illuminate our results.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, China

    Nan-Jing Huang

  2. Department of Mathematics, Sichuan University of Sciences and Engineering, Zigong, Sichuan, 643033, China

    Heng-You Lan

  3. Department of Mathematics and Statistics, Curtin University of Technology, Perth, 6102, Australia

    Kok Lay Teo

Authors
  1. Nan-Jing Huang
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  2. Heng-You Lan
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  3. Kok Lay Teo
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Correspondence to Nan-Jing Huang.

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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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Huang, NJ., Lan, HY. & Teo, K.L. On the Existence and Convergence of Approximate Solutions for Equilibrium Problems in Banach Spaces. J Inequal Appl 2007, 017294 (2007). https://doi.org/10.1155/2007/17294

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