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An algorithm for split equilibrium and fixed-point problems using inertial extragradient techniques

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Abstract

We study in this article, split equilibrium fixed-point problems involving pseudomonotone bifunctions which satisfy Lipschitz-type continuous condition and nonexpansive mappings, respectively, in real Hilbert spaces. In order to solve this problem, we propose an inertial extragradient algorithm and establish strong convergence theorem using the sequence of the algorithm under mild conditions. A numerical example given demonstrates that our algorithm is efficient and is superior to the algorithm studied by Narin (J Ineq Appl 2019:137, 2019).

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Acknowledgements

The second author thanks University of Hafr Al Batin for continuous support. The authors thank deeply the reviewers for thoroughly evaluating the original manuscript and making insightful comments that helped improve the quality of the paper.

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Author notes

  1. Cyril D. Enyi, Francis O. Nwawuru and Richard C. Ogbonna contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Port Harcourt, Port Harcourt, Nigeria

    Jeremiah N. Ezeora

  2. Department of Mathematics, University of Hafr Al Batin, Hafr Al Batin, Saudi Arabia

    Cyril D. Enyi

  3. Department of Mathematics, Chukwuemeka Odumegwu Ojukwu University, Awka, Anambra State, Nigeria

    Francis O. Nwawuru

  4. Department of Computer Science and Mathematics, Evangel University, Aka-Eze, Nigeria

    Richard C. Ogbonna

Authors
  1. Jeremiah N. Ezeora
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  2. Cyril D. Enyi
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  3. Francis O. Nwawuru
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  4. Richard C. Ogbonna
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Correspondence to Jeremiah N. Ezeora.

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Ezeora, J.N., Enyi, C.D., Nwawuru, F.O. et al. An algorithm for split equilibrium and fixed-point problems using inertial extragradient techniques. Comp. Appl. Math. 42, 103 (2023). https://doi.org/10.1007/s40314-023-02244-7

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  • DOI: https://doi.org/10.1007/s40314-023-02244-7

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