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A Projection-Type Implicit Algorithm for Finding a Common Solution for Fixed Point Problems and Variational Inequality Problems

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  • Vasile Berinde

    (Department of Mathematics and Computer Science, North University Centre at Baia Mare, Technical University of Cluj-Napoca, Victoriei 76, 430072 Baia Mare, Romania
    Academy of Romanian Scientists, 3 Ilfov, 050044 Bucharest, Romania)

Abstract

This paper deals with the problem of finding a common solution for a fixed point problem for strictly pseudocontractive mappings and for a certain variational inequality problem. We propose a projection-type implicit averaged algorithm and establish the strong convergence of the sequences generated by this method to the common solution for the fixed point problem and the variational inequality problem. In order to illustrate the feasibility of the hypotheses and the superiority of our theoretical results over the existing literature, an example is also presented.

Suggested Citation

  • Vasile Berinde, 2024. "A Projection-Type Implicit Algorithm for Finding a Common Solution for Fixed Point Problems and Variational Inequality Problems," Mathematics, MDPI, vol. 12(20), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3187-:d:1496796
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    References listed on IDEAS

    as
    1. W. Takahashi & M. Toyoda, 2003. "Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 417-428, August.
    2. Yeong-Cheng Liou, 2012. "Computing the Fixed Points of Strictly Pseudocontractive Mappings by the Implicit and Explicit Iterations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, July.
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