Abstract
The focus of this paper is to obtain weak and linear convergence analysis of the subgradient extragradient method with alternated inertial step for solving equilibrium problems in real Hilbert spaces. The proposed method uses self-adaptive step sizes. Weak convergence is established without Lipschitz constant of the bifunction as an input parameter. Linear convergence is obtained without the modulus of strong pseudomonotonicity and Lipschitz constant as input parameters. We report some priori and posteriori error estimates and some numerical experiments to illustrate the behavior of our proposed method with related methods.
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Acknowledgements
The authors are grateful to the anonymous referees and the associate editor for their comments and suggestions which have improved on the earlier version of the paper. This paper is dedicated to the loving memory of late Professor Charles Ejike Chidume (1947–2021).
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Shehu, Y., Dong, QL., Liu, L. et al. Alternated inertial subgradient extragradient method for equilibrium problems. TOP 31, 1–30 (2023). https://doi.org/10.1007/s11750-021-00620-2
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DOI: https://doi.org/10.1007/s11750-021-00620-2