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A General Iterative Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

Abstract

We introduce a general iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Our results improve and extend the corresponding ones announced by S. Takahashi and W. Takahashi in 2007, Marino and Xu in 2006, Combettes and Hirstoaga in 2005, and many others.

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Correspondence to Yongfu Su.

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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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Shang, M., Su, Y. & Qin, X. A General Iterative Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces. Fixed Point Theory Appl 2007, 095412 (2008). https://doi.org/10.1155/2007/95412

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