Viscosity-type method for solving pseudomonotone equilibrium problems in a real Hilbert space with applications

The aim of this article is to introduce a new algorithm by integrating a viscosity-type method with the subgradient extragradient algorithm to solve the equilibrium problems involving pseudomonotone and Lipschitz-type continuous bifunction in a real Hilbert space. A strong convergence theorem is pro...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 2; pp. 1538 - 1560
Main Authors ur Rehman, Habib, Kumam, Poom, Sitthithakerngkiet, Kanokwan
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
equilibrium problem
fixed point problems
lipschitz-like conditions
strong convergence
variational inequality problem
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ISSN2473-6988
2473-6988
DOI10.3934/math.2021093

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Summary:The aim of this article is to introduce a new algorithm by integrating a viscosity-type method with the subgradient extragradient algorithm to solve the equilibrium problems involving pseudomonotone and Lipschitz-type continuous bifunction in a real Hilbert space. A strong convergence theorem is proved by the use of certain mild conditions on the bifunction as well as some restrictions on the iterative control parameters. Applications of the main results are also presented to address variational inequalities and fixed-point problems. The computational behaviour of the proposed algorithm on various test problems is described in comparison to other existing algorithms.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021093