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Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach Space

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  • Wariam Chuayjan
  • Sornsak Thianwan

Abstract

We introduce and study a new hybrid projection algorithm for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of relatively quasi-nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly-monotone operator in a Banach space. Under suitable assumptions, we show a strong convergence theorem. Using this result, we obtain some applications in a Banach space. The results obtained in this paper extend and improve the several recent results in this area.

Suggested Citation

  • Wariam Chuayjan & Sornsak Thianwan, 2009. "Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach Space," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-22, October.
    • Handle: RePEc:hin:jnlaaa:613524
    DOI: 10.1155/2009/613524
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