An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces

An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces

In this paper, we propose an iterative scheme for a special split feasibility problem with the maximal monotone operator and fixed-point problem in Banach spaces. The algorithm implements Halpern’s iteration with an inertial technique for the problem. Under some mild assumption of the monotonicity o...

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Main Authors: Huijuan Jia, Shufen Liu, Yazheng Dang
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/9974351
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spelling doaj-2a3bf9af3aef42a185b0ee2f24477bc32021-05-24T00:15:05ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/9974351An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach SpacesHuijuan Jia0Shufen Liu1Yazheng Dang2College of Computer Science and TechnologyCollege of Computer Science and TechnologySchool of BusinessIn this paper, we propose an iterative scheme for a special split feasibility problem with the maximal monotone operator and fixed-point problem in Banach spaces. The algorithm implements Halpern’s iteration with an inertial technique for the problem. Under some mild assumption of the monotonicity of the related mapping, we establish the strong convergence of the sequence generated by the algorithm which does not require the spectral radius of ATA. Finally, the numerical example is presented to demonstrate the efficiency of the algorithm.http://dx.doi.org/10.1155/2021/9974351
collection DOAJ
language English
format Article
sources DOAJ
author Huijuan Jia
Shufen Liu
Yazheng Dang
spellingShingle Huijuan Jia
Shufen Liu
Yazheng Dang
An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces
Journal of Mathematics
author_facet Huijuan Jia
Shufen Liu
Yazheng Dang
author_sort Huijuan Jia
title An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces
title_short An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces
title_full An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces
title_fullStr An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces
title_full_unstemmed An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces
title_sort inertial iterative algorithm with strong convergence for solving modified split feasibility problem in banach spaces
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4785
publishDate 2021-01-01
description In this paper, we propose an iterative scheme for a special split feasibility problem with the maximal monotone operator and fixed-point problem in Banach spaces. The algorithm implements Halpern’s iteration with an inertial technique for the problem. Under some mild assumption of the monotonicity of the related mapping, we establish the strong convergence of the sequence generated by the algorithm which does not require the spectral radius of ATA. Finally, the numerical example is presented to demonstrate the efficiency of the algorithm.
url http://dx.doi.org/10.1155/2021/9974351
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AT shufenliu aninertialiterativealgorithmwithstrongconvergenceforsolvingmodifiedsplitfeasibilityprobleminbanachspaces
AT yazhengdang aninertialiterativealgorithmwithstrongconvergenceforsolvingmodifiedsplitfeasibilityprobleminbanachspaces
AT huijuanjia inertialiterativealgorithmwithstrongconvergenceforsolvingmodifiedsplitfeasibilityprobleminbanachspaces
AT shufenliu inertialiterativealgorithmwithstrongconvergenceforsolvingmodifiedsplitfeasibilityprobleminbanachspaces
AT yazhengdang inertialiterativealgorithmwithstrongconvergenceforsolvingmodifiedsplitfeasibilityprobleminbanachspaces
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