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Explicit Iteration Methods for Solving Variational Inequalities in Banach Spaces

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Abstract

The problem of finding a solution of a variational inequality over the set of common fixed points of a nonexpansive semigroup is considered in a real and uniformly convex Banach space without imposing the sequential weak continuity of the normalized duality mapping. Two new explicit iterative methods are introduced based on the steepest-descent method, and conditions are given to obtain their strong convergence. A numerical example is showed to illustrate the convergence analysis of the proposed methods.

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Acknowledgements

The authors are very grateful to the referees for their useful comments, which helped to improve the paper.

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Authors and Affiliations

  1. Faculty of Basic Science, University of Agriculture and Forestry, Thai Nguyen University, Quyet Thang Commune, Thai Nguyen City, Vietnam

    Pham Thanh Hieu

  2. Department of Mathematics and Informatics, University of Science, Thai Nguyen University, Tan Thinh Ward, Thai Nguyen City, Vietnam

    Nguyen Thi Thu Thuy

  3. Department of Mathematics, University of Namur, Namur, Belgium

    Jean Jacques Strodiot

Authors
  1. Pham Thanh Hieu
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  2. Nguyen Thi Thu Thuy
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  3. Jean Jacques Strodiot
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Correspondence to Jean Jacques Strodiot.

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Communicated by Poom Kumam.

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Hieu, P.T., Thuy, N.T.T. & Strodiot, J.J. Explicit Iteration Methods for Solving Variational Inequalities in Banach Spaces. Bull. Malays. Math. Sci. Soc. 42, 467–483 (2019). https://doi.org/10.1007/s40840-017-0494-8

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  • DOI: https://doi.org/10.1007/s40840-017-0494-8

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