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An Iteration Method for Common Solution of a System of Equilibrium Problems in Hilbert Spaces

Abstract

The strong convergence theorem is proved for finding a common solution for a system of equilibrium problems: find where is a closed convex subset of a Hilbert space and are bifunctions from into R given exactly or approximatively. As an application, finding a common solution for a system of variational inequality problems is given.

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Correspondence to Jong Kyu Kim.

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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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Kim, J.K., Buong, N. An Iteration Method for Common Solution of a System of Equilibrium Problems in Hilbert Spaces. Fixed Point Theory Appl 2011, 780764 (2011). https://doi.org/10.1155/2011/780764

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Keywords

  • Hilbert Space
  • Variational Inequality
  • Differential Geometry
  • Convex Subset
  • Convergence Theorem