Strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach space

Abstract We propose and analyze an inertial iterative algorithm to approximate a common solution of generalized equilibrium problem, variational inequality problem, and fixed point problem in the framework of a 2-uniformly convex and uniformly smooth real Banach space. Further, we study the converge...

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Main Authors:	Monairah Alansari, Rehan Ali, Mohammad Farid
Format:	Article
Language:	English
Published:	SpringerOpen 2020-02-01
Series:	Journal of Inequalities and Applications
Subjects:	Generalized equilibrium problem Variational inequality problem Relatively nonexpansive mapping Inertial hybrid iterative method
Online Access:	http://link.springer.com/article/10.1186/s13660-020-02313-z

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spelling	doaj-958b76d761e94b728208e5b7cf94f43b2020-11-25T03:37:04ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-02-012020112210.1186/s13660-020-02313-zStrong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach spaceMonairah Alansari0Rehan Ali1Mohammad Farid2King Abdulaziz UniversityDepartment of Mathematics, Jamia Millia IslamiaDeanship of Educational Services, Qassim UniversityAbstract We propose and analyze an inertial iterative algorithm to approximate a common solution of generalized equilibrium problem, variational inequality problem, and fixed point problem in the framework of a 2-uniformly convex and uniformly smooth real Banach space. Further, we study the convergence analysis of our proposed iterative method. Finally, we give application and a numerical example to illustrate the applicability of the main algorithm.http://link.springer.com/article/10.1186/s13660-020-02313-zGeneralized equilibrium problemVariational inequality problemRelatively nonexpansive mappingInertial hybrid iterative method
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Monairah Alansari Rehan Ali Mohammad Farid
spellingShingle	Monairah Alansari Rehan Ali Mohammad Farid Strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach space Journal of Inequalities and Applications Generalized equilibrium problem Variational inequality problem Relatively nonexpansive mapping Inertial hybrid iterative method
author_facet	Monairah Alansari Rehan Ali Mohammad Farid
author_sort	Monairah Alansari
title	Strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach space
title_short	Strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach space
title_full	Strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach space
title_fullStr	Strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach space
title_full_unstemmed	Strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach space
title_sort	strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a banach space
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2020-02-01
description	Abstract We propose and analyze an inertial iterative algorithm to approximate a common solution of generalized equilibrium problem, variational inequality problem, and fixed point problem in the framework of a 2-uniformly convex and uniformly smooth real Banach space. Further, we study the convergence analysis of our proposed iterative method. Finally, we give application and a numerical example to illustrate the applicability of the main algorithm.
topic	Generalized equilibrium problem Variational inequality problem Relatively nonexpansive mapping Inertial hybrid iterative method
url	http://link.springer.com/article/10.1186/s13660-020-02313-z
work_keys_str_mv	AT monairahalansari strongconvergenceofaninertialiterativealgorithmforvariationalinequalityproblemgeneralizedequilibriumproblemandfixedpointprobleminabanachspace AT rehanali strongconvergenceofaninertialiterativealgorithmforvariationalinequalityproblemgeneralizedequilibriumproblemandfixedpointprobleminabanachspace AT mohammadfarid strongconvergenceofaninertialiterativealgorithmforvariationalinequalityproblemgeneralizedequilibriumproblemandfixedpointprobleminabanachspace
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Strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach space

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