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The Shrinking Projection Method for Solving Variational Inequality Problems and Fixed Point Problems in Banach Spaces

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  • Rabian Wangkeeree
  • Rattanaporn Wangkeeree

Abstract

We consider a hybrid projection algorithm based on the shrinking projection method for two families of quasi- -nonexpansive mappings. We establish strong convergence theorems for approximating the common element of the set of the common fixed points of such two families and the set of solutions of the variational inequality for an inverse-strongly monotone operator in the framework of Banach spaces. As applications, at the end of the paper we first apply our results to consider the problem of finding a zero point of an inverse-strongly monotone operator and we finally utilize our results to study the problem of finding a solution of the complementarity problem. Our results improve and extend the corresponding results announced by recent results.

Suggested Citation

  • Rabian Wangkeeree & Rattanaporn Wangkeeree, 2009. "The Shrinking Projection Method for Solving Variational Inequality Problems and Fixed Point Problems in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-26, November.
    • Handle: RePEc:hin:jnlaaa:624798
    DOI: 10.1155/2009/624798
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    Cited by:

    1. Yekini Shehu, 2011. "Strong Convergence Theorems for Family of Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems and Variational Inequality Problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-22, April.

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