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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Vydáno v:AIMS mathematics Ročník 6; číslo 2; s. 1538 - 1560
Hlavní autoři: ur Rehman, Habib, Kumam, Poom, Sitthithakerngkiet, Kanokwan
Médium: Journal Article
Jazyk:angličtina
Vydáno: AIMS Press 01.01.2021
Témata:
equilibrium problem
fixed point problems
lipschitz-like conditions
strong convergence
variational inequality problem
ISSN:2473-6988, 2473-6988
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Abstract 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.
AbstractList 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.
Author ur Rehman, Habib
Kumam, Poom
Sitthithakerngkiet, Kanokwan
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CorporateAuthor 1 KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
2 Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
3 Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Bangkok, Thailand
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SubjectTerms equilibrium problem
fixed point problems
lipschitz-like conditions
strong convergence
variational inequality problem
Title Viscosity-type method for solving pseudomonotone equilibrium problems in a real Hilbert space with applications
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