The Generalized Implicit Iterative Process for Approximating Fixed Points of Nonexpansive Mappings in CAT(0) Spaces

The aim of this paper is to investigate implicit viscosity iterative algorithm for nonexpansive mappings in the framework of CAT(0) spaces. We prove strong convergence theorems of such algorithm under some suitable assumptions on the sequences of parameters involved therein. We also proved that the...

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Main Authors: Xingchao Bian, Sundus Shahzeen, Mujahid Abbas, M. Saeed Ahmad, Binli Zhang
Format: Article
Language:English
Published: IEEE 2020-01-01
Series:IEEE Access
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Online Access:https://ieeexplore.ieee.org/document/8945216/
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author Xingchao Bian
Sundus Shahzeen
Mujahid Abbas
M. Saeed Ahmad
Binli Zhang
author_facet Xingchao Bian
Sundus Shahzeen
Mujahid Abbas
M. Saeed Ahmad
Binli Zhang
author_sort Xingchao Bian
collection DOAJ
description The aim of this paper is to investigate implicit viscosity iterative algorithm for nonexpansive mappings in the framework of CAT(0) spaces. We prove strong convergence theorems of such algorithm under some suitable assumptions on the sequences of parameters involved therein. We also proved that the presented algorithm is faster than a number of existing iteration processes in literature. Our results extend and improve some recent results of Ahmad et al.[J. Appl. Math. Informatics 35 (5-6)(2017), 423-438] and others.
format Article
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institution Kabale University
issn 2169-3536
language English
publishDate 2020-01-01
publisher IEEE
record_format Article
series IEEE Access
spelling doaj-art-01d74f89938846feb872d418fa9da5832025-08-22T23:09:32ZengIEEEIEEE Access2169-35362020-01-0187423743410.1109/ACCESS.2019.29630248945216The Generalized Implicit Iterative Process for Approximating Fixed Points of Nonexpansive Mappings in CAT(0) SpacesXingchao Bian0https://orcid.org/0000-0002-7580-5992Sundus Shahzeen1https://orcid.org/0000-0002-8087-3228Mujahid Abbas2https://orcid.org/0000-0001-5528-1207M. Saeed Ahmad3https://orcid.org/0000-0002-8706-3711Binli Zhang4https://orcid.org/0000-0002-6627-1343College of Information Engineering, Suihua University, Suihua, ChinaDepartment of Mathematics and Statistics, The University of Lahore, Lahore, PakistanDepartment of Mathematics, Government College University, Lahore, PakistanDepartment of Mathematics, Government College University, Lahore, PakistanInstitute of Economic Management, Suihua University, Suihua, ChinaThe aim of this paper is to investigate implicit viscosity iterative algorithm for nonexpansive mappings in the framework of CAT(0) spaces. We prove strong convergence theorems of such algorithm under some suitable assumptions on the sequences of parameters involved therein. We also proved that the presented algorithm is faster than a number of existing iteration processes in literature. Our results extend and improve some recent results of Ahmad et al.[J. Appl. Math. Informatics 35 (5-6)(2017), 423-438] and others.https://ieeexplore.ieee.org/document/8945216/Viscosity iterative algorithmCAT(0) spacenonexpansive mappingvariational inequality
spellingShingle Xingchao Bian
Sundus Shahzeen
Mujahid Abbas
M. Saeed Ahmad
Binli Zhang
The Generalized Implicit Iterative Process for Approximating Fixed Points of Nonexpansive Mappings in CAT(0) Spaces
IEEE Access
Viscosity iterative algorithm
CAT(0) space
nonexpansive mapping
variational inequality
title The Generalized Implicit Iterative Process for Approximating Fixed Points of Nonexpansive Mappings in CAT(0) Spaces
title_full The Generalized Implicit Iterative Process for Approximating Fixed Points of Nonexpansive Mappings in CAT(0) Spaces
title_fullStr The Generalized Implicit Iterative Process for Approximating Fixed Points of Nonexpansive Mappings in CAT(0) Spaces
title_full_unstemmed The Generalized Implicit Iterative Process for Approximating Fixed Points of Nonexpansive Mappings in CAT(0) Spaces
title_short The Generalized Implicit Iterative Process for Approximating Fixed Points of Nonexpansive Mappings in CAT(0) Spaces
title_sort generalized implicit iterative process for approximating fixed points of nonexpansive mappings in cat 0 spaces
topic Viscosity iterative algorithm
CAT(0) space
nonexpansive mapping
variational inequality
url https://ieeexplore.ieee.org/document/8945216/
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