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An inertial method for solving split equality quasimonotone Minty variational inequality problems in reflexive Banach spaces

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Abstract

In this paper, we introduce the split equality Minty variational inequality problem in reflexive real Banach spaces. Then we construct a single projection inertial algorithm for solving the introduced problem. We establish a strong convergence result with the assumption that the mappings under consideration are Lipschitz continuous and quasimonotone. We give some specific applications of the main result and finally provide a numerical example to demonstrate the workability of our method.

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Acknowledgements

The first and second authors gratefully acknowledge the funding received from Simons Foundation based at Botswana International University of Science and Technology (BIUST). The first author is grateful to Aksum University for the financial support provided during his study.

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Authors and Affiliations

  1. Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Pvt. Bag 0016, Palapye, Botswana

    Yirga A. Belay, Habtu Zegeye, Oganeditse A. Boikanyo, Hagos H. Gidey & Dintle Kagiso

  2. Department of Mathematics, Aksum University, P.O. Box 1010, Axum, Ethiopia

    Yirga A. Belay

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  1. Yirga A. Belay
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  2. Habtu Zegeye
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  3. Oganeditse A. Boikanyo
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Correspondence to Habtu Zegeye.

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Belay, Y.A., Zegeye, H., Boikanyo, O.A. et al. An inertial method for solving split equality quasimonotone Minty variational inequality problems in reflexive Banach spaces. Rend. Circ. Mat. Palermo, II. Ser (2024). https://doi.org/10.1007/s12215-024-01025-3

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