Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications

The aim of this paper is to propose two new modified extragradient methods to solve the pseudo-monotone equilibrium problem in a real Hilbert space with the Lipschitz-type condition. The iterative schemes use a new step size rule that is updated on each iteration based on the value of previous itera...

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Autores principales:	Pakkaranang Nuttapol, Rehman Habib ur, Kumam Wiyada
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	equilibrium problem pseudomonotone bifunction lipschitz-type conditions strong convergence variational inequality problems fixed point problem 47j25 47h09 47h06 47j05 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/7e43da8bd1de4736a2b0a6795810ce7f
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id	oai:doaj.org-article:7e43da8bd1de4736a2b0a6795810ce7f
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spelling	oai:doaj.org-article:7e43da8bd1de4736a2b0a6795810ce7f2021-12-05T14:10:45ZTwo strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications2391-466110.1515/dema-2021-0030https://doaj.org/article/7e43da8bd1de4736a2b0a6795810ce7f2021-08-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0030https://doaj.org/toc/2391-4661The aim of this paper is to propose two new modified extragradient methods to solve the pseudo-monotone equilibrium problem in a real Hilbert space with the Lipschitz-type condition. The iterative schemes use a new step size rule that is updated on each iteration based on the value of previous iterations. By using mild conditions on a bi-function, two strong convergence theorems are established. The applications of proposed results are studied to solve variational inequalities and fixed point problems in the setting of real Hilbert spaces. Many numerical experiments have been provided in order to show the algorithmic performance of the proposed methods and compare them with the existing ones.Pakkaranang NuttapolRehman Habib urKumam WiyadaDe Gruyterarticleequilibrium problempseudomonotone bifunctionlipschitz-type conditionsstrong convergencevariational inequality problemsfixed point problem47j2547h0947h0647j05MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 280-298 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	equilibrium problem pseudomonotone bifunction lipschitz-type conditions strong convergence variational inequality problems fixed point problem 47j25 47h09 47h06 47j05 Mathematics QA1-939
spellingShingle	equilibrium problem pseudomonotone bifunction lipschitz-type conditions strong convergence variational inequality problems fixed point problem 47j25 47h09 47h06 47j05 Mathematics QA1-939 Pakkaranang Nuttapol Rehman Habib ur Kumam Wiyada Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications
description	The aim of this paper is to propose two new modified extragradient methods to solve the pseudo-monotone equilibrium problem in a real Hilbert space with the Lipschitz-type condition. The iterative schemes use a new step size rule that is updated on each iteration based on the value of previous iterations. By using mild conditions on a bi-function, two strong convergence theorems are established. The applications of proposed results are studied to solve variational inequalities and fixed point problems in the setting of real Hilbert spaces. Many numerical experiments have been provided in order to show the algorithmic performance of the proposed methods and compare them with the existing ones.
format	article
author	Pakkaranang Nuttapol Rehman Habib ur Kumam Wiyada
author_facet	Pakkaranang Nuttapol Rehman Habib ur Kumam Wiyada
author_sort	Pakkaranang Nuttapol
title	Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications
title_short	Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications
title_full	Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications
title_fullStr	Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications
title_full_unstemmed	Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications
title_sort	two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/7e43da8bd1de4736a2b0a6795810ce7f
work_keys_str_mv	AT pakkaranangnuttapol twostronglyconvergentselfadaptiveiterativeschemesforsolvingpseudomonotoneequilibriumproblemswithapplications AT rehmanhabibur twostronglyconvergentselfadaptiveiterativeschemesforsolvingpseudomonotoneequilibriumproblemswithapplications AT kumamwiyada twostronglyconvergentselfadaptiveiterativeschemesforsolvingpseudomonotoneequilibriumproblemswithapplications
_version_	1718371764295172096

Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications

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