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

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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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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Keywords

  • Banach Space
  • Exact Solution
  • Approximate Solution
  • Equilibrium Problem
  • Strong Convergence
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