A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications

Abstract An inertial iterative algorithm for approximating a point in the set of zeros of a maximal monotone operator which is also a common fixed point of a countable family of relatively nonexpansive operators is studied. Strong convergence theorem is proved in a uniformly convex and uniformly smo...

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Autores principales:	Charles E. Chidume, Poom Kumam, Abubakar Adamu
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2020
Materias:	Inertial Maximal monotone Fixed point Hybrid Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/371af04549ac430095a86c6b56d266be
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spelling	oai:doaj.org-article:371af04549ac430095a86c6b56d266be2021-12-02T12:35:57ZA hybrid inertial algorithm for approximating solution of convex feasibility problems with applications10.1186/s13663-020-00678-w1687-1812https://doaj.org/article/371af04549ac430095a86c6b56d266be2020-08-01T00:00:00Zhttp://link.springer.com/article/10.1186/s13663-020-00678-whttps://doaj.org/toc/1687-1812Abstract An inertial iterative algorithm for approximating a point in the set of zeros of a maximal monotone operator which is also a common fixed point of a countable family of relatively nonexpansive operators is studied. Strong convergence theorem is proved in a uniformly convex and uniformly smooth real Banach space. This theorem extends, generalizes and complements several recent important results. Furthermore, the theorem is applied to convex optimization problems and to J-fixed point problems. Finally, some numerical examples are presented to show the effect of the inertial term in the convergence of the sequence of the algorithm.Charles E. ChidumePoom KumamAbubakar AdamuSpringerOpenarticleInertialMaximal monotoneFixed pointHybridApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Applications, Vol 2020, Iss 1, Pp 1-17 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Inertial Maximal monotone Fixed point Hybrid Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
spellingShingle	Inertial Maximal monotone Fixed point Hybrid Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433 Charles E. Chidume Poom Kumam Abubakar Adamu A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications
description	Abstract An inertial iterative algorithm for approximating a point in the set of zeros of a maximal monotone operator which is also a common fixed point of a countable family of relatively nonexpansive operators is studied. Strong convergence theorem is proved in a uniformly convex and uniformly smooth real Banach space. This theorem extends, generalizes and complements several recent important results. Furthermore, the theorem is applied to convex optimization problems and to J-fixed point problems. Finally, some numerical examples are presented to show the effect of the inertial term in the convergence of the sequence of the algorithm.
format	article
author	Charles E. Chidume Poom Kumam Abubakar Adamu
author_facet	Charles E. Chidume Poom Kumam Abubakar Adamu
author_sort	Charles E. Chidume
title	A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications
title_short	A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications
title_full	A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications
title_fullStr	A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications
title_full_unstemmed	A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications
title_sort	hybrid inertial algorithm for approximating solution of convex feasibility problems with applications
publisher	SpringerOpen
publishDate	2020
url	https://doaj.org/article/371af04549ac430095a86c6b56d266be
work_keys_str_mv	AT charlesechidume ahybridinertialalgorithmforapproximatingsolutionofconvexfeasibilityproblemswithapplications AT poomkumam ahybridinertialalgorithmforapproximatingsolutionofconvexfeasibilityproblemswithapplications AT abubakaradamu ahybridinertialalgorithmforapproximatingsolutionofconvexfeasibilityproblemswithapplications AT charlesechidume hybridinertialalgorithmforapproximatingsolutionofconvexfeasibilityproblemswithapplications AT poomkumam hybridinertialalgorithmforapproximatingsolutionofconvexfeasibilityproblemswithapplications AT abubakaradamu hybridinertialalgorithmforapproximatingsolutionofconvexfeasibilityproblemswithapplications
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A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications

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