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Common Solutions of an Iterative Scheme for Variational Inclusions, Equilibrium Problems, and Fixed Point Problems

Abstract

We introduce an iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of a variational inclusion with set-valued maximal monotone mapping and inverse strongly monotone mappings, the set of solutions of an equilibrium problem, and the set of fixed points of a nonexpansive mapping. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. The results in this paper unify, extend, and improve some well-known results in the literature.

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Correspondence to David S. Shyu.

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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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Peng, JW., Wang, Y., Shyu, D.S. et al. Common Solutions of an Iterative Scheme for Variational Inclusions, Equilibrium Problems, and Fixed Point Problems. J Inequal Appl 2008, 720371 (2008). https://doi.org/10.1155/2008/720371

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  • DOI: https://doi.org/10.1155/2008/720371

Keywords

  • Hilbert Space
  • Convergence Theorem
  • Equilibrium Problem
  • Monotone Mapping
  • Nonexpansive Mapping