A simple computational algorithm with inertial extrapolation for generalized split common fixed point problems

In the present paper, we explore operator norm independent inertial type accelerated iterative algorithm solving generalized split common fixed point problem, which is the problem of finding a point that belongs to the intersection of a finite family of fixed point sets of demimetric mappings such t...

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Autores principales:	Anteneh Getachew Gebrie, Dejene Shewakena Bedane
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Split common fixed-point problem κ-demimetric mapping Inertial method Strong convergence Hilbert space Science (General) Q1-390 Social sciences (General) H1-99
Acceso en línea:	https://doaj.org/article/c23d65f949bd4de0b53078032383ec18
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id	oai:doaj.org-article:c23d65f949bd4de0b53078032383ec18
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spelling	oai:doaj.org-article:c23d65f949bd4de0b53078032383ec182021-12-02T05:02:54ZA simple computational algorithm with inertial extrapolation for generalized split common fixed point problems2405-844010.1016/j.heliyon.2021.e08373https://doaj.org/article/c23d65f949bd4de0b53078032383ec182021-11-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2405844021024762https://doaj.org/toc/2405-8440In the present paper, we explore operator norm independent inertial type accelerated iterative algorithm solving generalized split common fixed point problem, which is the problem of finding a point that belongs to the intersection of a finite family of fixed point sets of demimetric mappings such that its image under a finite number of linear transformations belongs to the intersection of another finite family of fixed point sets of demimetric mappings in the image space. We adopt rules for selecting the step size such that the implementation of our proposed algorithm does not need any prior information about the operator norms. The strong convergence result is analyzed and some applications of our proposed algorithm are demonstrated. Our result in this paper will improve and generalize many results in the literature. Numerical experiments show that our iteration method is very effective for approximating the solution point of problem under consideration.Anteneh Getachew GebrieDejene Shewakena BedaneElsevierarticleSplit common fixed-point problemκ-demimetric mappingInertial methodStrong convergenceHilbert spaceScience (General)Q1-390Social sciences (General)H1-99ENHeliyon, Vol 7, Iss 11, Pp e08373- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Split common fixed-point problem κ-demimetric mapping Inertial method Strong convergence Hilbert space Science (General) Q1-390 Social sciences (General) H1-99
spellingShingle	Split common fixed-point problem κ-demimetric mapping Inertial method Strong convergence Hilbert space Science (General) Q1-390 Social sciences (General) H1-99 Anteneh Getachew Gebrie Dejene Shewakena Bedane A simple computational algorithm with inertial extrapolation for generalized split common fixed point problems
description	In the present paper, we explore operator norm independent inertial type accelerated iterative algorithm solving generalized split common fixed point problem, which is the problem of finding a point that belongs to the intersection of a finite family of fixed point sets of demimetric mappings such that its image under a finite number of linear transformations belongs to the intersection of another finite family of fixed point sets of demimetric mappings in the image space. We adopt rules for selecting the step size such that the implementation of our proposed algorithm does not need any prior information about the operator norms. The strong convergence result is analyzed and some applications of our proposed algorithm are demonstrated. Our result in this paper will improve and generalize many results in the literature. Numerical experiments show that our iteration method is very effective for approximating the solution point of problem under consideration.
format	article
author	Anteneh Getachew Gebrie Dejene Shewakena Bedane
author_facet	Anteneh Getachew Gebrie Dejene Shewakena Bedane
author_sort	Anteneh Getachew Gebrie
title	A simple computational algorithm with inertial extrapolation for generalized split common fixed point problems
title_short	A simple computational algorithm with inertial extrapolation for generalized split common fixed point problems
title_full	A simple computational algorithm with inertial extrapolation for generalized split common fixed point problems
title_fullStr	A simple computational algorithm with inertial extrapolation for generalized split common fixed point problems
title_full_unstemmed	A simple computational algorithm with inertial extrapolation for generalized split common fixed point problems
title_sort	simple computational algorithm with inertial extrapolation for generalized split common fixed point problems
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/c23d65f949bd4de0b53078032383ec18
work_keys_str_mv	AT antenehgetachewgebrie asimplecomputationalalgorithmwithinertialextrapolationforgeneralizedsplitcommonfixedpointproblems AT dejeneshewakenabedane asimplecomputationalalgorithmwithinertialextrapolationforgeneralizedsplitcommonfixedpointproblems AT antenehgetachewgebrie simplecomputationalalgorithmwithinertialextrapolationforgeneralizedsplitcommonfixedpointproblems AT dejeneshewakenabedane simplecomputationalalgorithmwithinertialextrapolationforgeneralizedsplitcommonfixedpointproblems
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A simple computational algorithm with inertial extrapolation for generalized split common fixed point problems

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