The generalized implicit iterative process for approximating fixed points of nonexpansive mappings in CAT(0) Spaces

Xingchao Bian; Sundus Shahzeen; Mujahid Abbas; M. Saeed Ahmad; Binli Zhang

doi:10.1109/ACCESS.2019.2963024

The generalized implicit iterative process for approximating fixed points of nonexpansive mappings in CAT(0) Spaces

Xingchao Bian
, Sundus Shahzeen
, Mujahid Abbas
, M. Saeed Ahmad
, Binli Zhang

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	8945216
Pages (from-to)	7423-7434
Number of pages	12
Journal	IEEE Access
Volume	8
DOIs	https://doi.org/10.1109/ACCESS.2019.2963024
Publication status	Published - 2020
Externally published	Yes

Keywords

CAT(0) space
nonexpansive mapping
variational inequality
Viscosity iterative algorithm

ASJC Scopus subject areas

General Computer Science
General Materials Science
General Engineering
Electrical and Electronic Engineering

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10.1109/ACCESS.2019.2963024

Cite this

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title = "The generalized implicit iterative process for approximating fixed points of nonexpansive mappings in CAT(0) Spaces",

abstract = "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.",

keywords = "CAT(0) space, nonexpansive mapping, variational inequality, Viscosity iterative algorithm",

author = "Xingchao Bian and Sundus Shahzeen and Mujahid Abbas and Ahmad, \{M. Saeed\} and Binli Zhang",

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year = "2020",

doi = "10.1109/ACCESS.2019.2963024",

language = "English",

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AU - Bian, Xingchao

AU - Shahzeen, Sundus

AU - Abbas, Mujahid

AU - Ahmad, M. Saeed

AU - Zhang, Binli

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - CAT(0) space

KW - nonexpansive mapping

KW - variational inequality

KW - Viscosity iterative algorithm

UR - https://www.scopus.com/pages/publications/85078315318

U2 - 10.1109/ACCESS.2019.2963024

DO - 10.1109/ACCESS.2019.2963024

M3 - Article

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JO - IEEE Access

JF - IEEE Access

M1 - 8945216

ER -

The generalized implicit iterative process for approximating fixed points of nonexpansive mappings in CAT(0) Spaces

Abstract

Keywords

ASJC Scopus subject areas

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