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A Fixed Point Scheme for Nonexpansive Mappings, Variational Inequalities and Equilibrium Problems

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Abstract

The purpose of this paper is to introduce a new iteration scheme and prove a strong convergence theorem for finding a common element of the fixed point set of a nonexpansive mapping, the solution set of variational inequalities and the solution set of equilibrium problems. Under certain conditions on parameters, we show that the iterative sequences generated by the scheme strongly converge to a common element in a real Hilbert space.

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Acknowledgements

This work is supported by the Vietnam Institute for Advanced Study in Mathematics.

We are very grateful to two anonymous referees for their really helpful and constructive comments on improving the paper.

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Authors and Affiliations

  1. Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam

    Pham N. Anh

  2. School of Applied Mathematics and Informatics, Ha Noi University of Science and Technology, No. 1, Dai Co Viet Road, Hai Ba Trung, Hanoi, Vietnam

    Le Q. Thuy

  3. Department of Mathematics, Haiphong University, Haiphong, Vietnam

    Do D. Thanh

Authors
  1. Pham N. Anh
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  2. Le Q. Thuy
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  3. Do D. Thanh
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Correspondence to Pham N. Anh.

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Anh, P.N., Thuy, L.Q. & Thanh, D.D. A Fixed Point Scheme for Nonexpansive Mappings, Variational Inequalities and Equilibrium Problems. Vietnam J. Math. 43, 71–91 (2015). https://doi.org/10.1007/s10013-014-0068-0

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  • DOI: https://doi.org/10.1007/s10013-014-0068-0

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