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An explicit subgradient extragradient algorithm with self-adaptive stepsize for pseudomonotone equilibrium problems in Banach spaces

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Abstract

In this paper, we introduce an explicit subgradient extragradient algorithm for solving equilibrium problem with a bifunction satisfying pseudomonotone and Lipschitz-like condition in a 2-uniformly convex and uniformly smooth Banach space. We also defined a new self-adaptive stepsize rule and prove a convergence result for solving the equilibrium problem without any prior estimate of the Lipschitz-like constants of the bifunction. Furthermore, we provide some numerical examples to illustrate the efficiency and accuracy of the proposed algorithm. This result improves and extends many recent results in this direction in the literature.

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Acknowledgments

The authors acknowledge the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University for making their facilities available for the research. The authors also acknowledge the financial support from the Research Office, Sefako Makgatho Health Sciences University, South Africa. The authors sincerely thank the anonymous reviewers whose comments have improved the content of this paper.

Funding

L.O. Jolaoso is supported by the Postdoctoral research funding from the Research Office, Sefako Makgatho Health Sciences University, South Africa.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Medunsa, 0204, Pretoria, South Africa

    Lateef Olakunle Jolaoso & Maggie Aphane

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  1. Lateef Olakunle Jolaoso
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  2. Maggie Aphane
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Correspondence to Lateef Olakunle Jolaoso.

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Jolaoso, L.O., Aphane, M. An explicit subgradient extragradient algorithm with self-adaptive stepsize for pseudomonotone equilibrium problems in Banach spaces. Numer Algor 89, 583–610 (2022). https://doi.org/10.1007/s11075-021-01126-5

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