Shrinking Extragradient Method for Pseudomonotone Equilibrium Problems and Quasi-Nonexpansive Mappings

Shrinking Extragradient Method for Pseudomonotone Equilibrium Problems and Quasi-Nonexpansive Mappings

This paper presents two shrinking extragradient algorithms that can both find the solution sets of equilibrium problems for pseudomonotone bifunctions and find the sets of fixed points of quasi-nonexpansive mappings in a real Hilbert space. Under some constraint qualifications of the scalar sequence...

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Main Authors: Manatchanok Khonchaliew, Ali Farajzadeh, Narin Petrot
Format: Article
Language:English
Published: MDPI AG 2019-04-01
Series:Symmetry
Subjects:
equilibrium problem
pseudomonotone bifunction
quasi-nonexpansive mapping
shrinking method
Online Access:https://www.mdpi.com/2073-8994/11/4/480
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spelling doaj-fd37b9283f3f4f208c5ab8f0e456a65c2020-11-24T20:41:56ZengMDPI AGSymmetry2073-89942019-04-0111448010.3390/sym11040480sym11040480Shrinking Extragradient Method for Pseudomonotone Equilibrium Problems and Quasi-Nonexpansive MappingsManatchanok Khonchaliew0Ali Farajzadeh1Narin Petrot2Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandDepartment of Mathematics, Razi University, Kermanshah 67149, IranDepartment of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandThis paper presents two shrinking extragradient algorithms that can both find the solution sets of equilibrium problems for pseudomonotone bifunctions and find the sets of fixed points of quasi-nonexpansive mappings in a real Hilbert space. Under some constraint qualifications of the scalar sequences, these two new algorithms show strong convergence. Some numerical experiments are presented to demonstrate the new algorithms. Finally, the two introduced algorithms are compared with a standard, well-known algorithm.https://www.mdpi.com/2073-8994/11/4/480equilibrium problempseudomonotone bifunctionquasi-nonexpansive mappingshrinking method
collection DOAJ
language English
format Article
sources DOAJ
author Manatchanok Khonchaliew
Ali Farajzadeh
Narin Petrot
spellingShingle Manatchanok Khonchaliew
Ali Farajzadeh
Narin Petrot
Shrinking Extragradient Method for Pseudomonotone Equilibrium Problems and Quasi-Nonexpansive Mappings
Symmetry
equilibrium problem
pseudomonotone bifunction
quasi-nonexpansive mapping
shrinking method
author_facet Manatchanok Khonchaliew
Ali Farajzadeh
Narin Petrot
author_sort Manatchanok Khonchaliew
title Shrinking Extragradient Method for Pseudomonotone Equilibrium Problems and Quasi-Nonexpansive Mappings
title_short Shrinking Extragradient Method for Pseudomonotone Equilibrium Problems and Quasi-Nonexpansive Mappings
title_full Shrinking Extragradient Method for Pseudomonotone Equilibrium Problems and Quasi-Nonexpansive Mappings
title_fullStr Shrinking Extragradient Method for Pseudomonotone Equilibrium Problems and Quasi-Nonexpansive Mappings
title_full_unstemmed Shrinking Extragradient Method for Pseudomonotone Equilibrium Problems and Quasi-Nonexpansive Mappings
title_sort shrinking extragradient method for pseudomonotone equilibrium problems and quasi-nonexpansive mappings
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2019-04-01
description This paper presents two shrinking extragradient algorithms that can both find the solution sets of equilibrium problems for pseudomonotone bifunctions and find the sets of fixed points of quasi-nonexpansive mappings in a real Hilbert space. Under some constraint qualifications of the scalar sequences, these two new algorithms show strong convergence. Some numerical experiments are presented to demonstrate the new algorithms. Finally, the two introduced algorithms are compared with a standard, well-known algorithm.
topic equilibrium problem
pseudomonotone bifunction
quasi-nonexpansive mapping
shrinking method
url https://www.mdpi.com/2073-8994/11/4/480
work_keys_str_mv AT manatchanokkhonchaliew shrinkingextragradientmethodforpseudomonotoneequilibriumproblemsandquasinonexpansivemappings
AT alifarajzadeh shrinkingextragradientmethodforpseudomonotoneequilibriumproblemsandquasinonexpansivemappings
AT narinpetrot shrinkingextragradientmethodforpseudomonotoneequilibriumproblemsandquasinonexpansivemappings
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