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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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| 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 |
| id | doaj-art-01d74f89938846feb872d418fa9da583 |
| 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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