A strong convergence theorem for solving pseudo-monotone variational inequalities and fixed point problems using subgradient extragradient method in Banach spaces

In this paper, we introduce an algorithm for solving variational inequalities problem with Lipschitz continuous and pseudomonotone mapping in Banach space. We modify the subgradient extragradient method with a new and simple iterative step size, and the strong convergence to a common solution of the...

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Bibliographic Details
Published inAIMS mathematics Vol. 7; no. 4; pp. 5015 - 5028
Main Authors Ma, Fei, Yang, Jun, Yin, Min
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
banach space
fixed point problem
strong convergence
subgradient extragradient method
variational inequalities
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Summary:In this paper, we introduce an algorithm for solving variational inequalities problem with Lipschitz continuous and pseudomonotone mapping in Banach space. We modify the subgradient extragradient method with a new and simple iterative step size, and the strong convergence to a common solution of the variational inequalities and fixed point problems is established without the knowledge of the Lipschitz constant. Finally, a numerical experiment is given in support of our results.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2022279