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Approximation of common solutions of nonlinear problems in Banach spaces

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Abstract

In this article, we propose hybrid projection iterative algorithm for finding a common element of solution set of a finite family of generalized mixed equilibrium problem, semi-fixed point set of a finite family of continuous semi-pseudocontractive mappings and solution set of a finite family of variational inequality for a finite family of monotone and L-Lipschitz mappings in Banach spaces and proved strong convergence theorem. The main result of the article generalizes some of known results in the literature. Furthermore, we give a numerical example to demonstrate the behavior of the convergence of the algorithm.

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Acknowledgements

This work was supported by Simons Foundation funded project based at Botswana International University of Science and Technology (BIUST), Palapye, Botswana (Grant No: ID267269FY17). The first author was also supported by the International Science Program(ISP)- Sweden, based in the Department of Mathematics, Addis Ababa University, Ethiopia.

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Authors and Affiliations

  1. Department of Mathematics, College of Natural and Computational Sciences, Addis Ababa University, P.O.Box 31167, Addis Ababa, Ethiopia

    Solomon B. Zegeye

  2. Department of Mathematics, Faculty of Sciences, University of Botswana, Pvt Bag 00704, Gaborone, Botswana

    Mengistu G. Sangago

  3. Department of Mathematics and Statistical Sciences, Faculty of Sciences, Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana

    Habtu Zegeye

Authors
  1. Solomon B. Zegeye
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  2. Mengistu G. Sangago
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  3. Habtu Zegeye
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Correspondence to Habtu Zegeye.

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Communicated by Joerg Fliege.

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Zegeye, S.B., Sangago, M.G. & Zegeye, H. Approximation of common solutions of nonlinear problems in Banach spaces. Comp. Appl. Math. 41, 200 (2022). https://doi.org/10.1007/s40314-022-01907-1

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  • DOI: https://doi.org/10.1007/s40314-022-01907-1

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