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An Iterative Method for Finding Common Solution of the Fixed Point Problem of a Finite Family of Nonexpansive Mappings and a Finite Family of Variational Inequality Problems in Hilbert Space

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  • Shamshad Husain
  • Nisha Singh

Abstract

In this paper, a hybrid iterative algorithm is proposed for finding a common element of the set of common fixed points of finite family of nonexpansive mappings and the set of common solutions of the variational inequality for an inverse strongly monotone mapping on the real Hilbert space. We establish the strong convergence of the proposed method for approximating a common element of the above defined sets under some suitable conditions. The results presented in this paper extend and improve some well-known corresponding results in the earlier and recent literature.

Suggested Citation

  • Shamshad Husain & Nisha Singh, 2019. "An Iterative Method for Finding Common Solution of the Fixed Point Problem of a Finite Family of Nonexpansive Mappings and a Finite Family of Variational Inequality Problems in Hilbert Space," Journal of Applied Mathematics, Hindawi, vol. 2019, pages 1-11, January.
    • Handle: RePEc:hin:jnljam:6875789
    DOI: 10.1155/2019/6875789
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