Strong and ▵ -convergence of Moudafi’s iterative algorithm for generalized nonexpansive mappings in convex metric spaces

Hafiz Fukhar-ud-din; Abdul Rahim Khan

doi:10.1007/s12215-019-00418-z

Strong and ▵ -convergence of Moudafi’s iterative algorithm for generalized nonexpansive mappings in convex metric spaces

Hafiz Fukhar-ud-din^*, Abdul Rahim Khan

^*Corresponding author for this work

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

2 Scopus citations

Abstract

We study Moudafi’s iterative algorithm for an α-nonexpansive mapping and a fundamentally nonexpansive mapping in the framework of a convex metric space. We prove ▵-convergence and strong convergence results for the algorithm to a common fixed point of the mappings. Our results are new and are also valid in CAT(0) spaces and Banach spaces, simultaneously.

Original language	English
Pages (from-to)	547-559
Number of pages	13
Journal	Rendiconti del Circolo Matematico di Palermo
Volume	69
Issue number	2
DOIs	https://doi.org/10.1007/s12215-019-00418-z
State	Published - 1 Aug 2020

Bibliographical note

Publisher Copyright:
© 2019, Springer-Verlag Italia S.r.l., part of Springer Nature.

Keywords

Common fixed point
Convergence
Convex metric space
Fundamentally nonexpansive mapping
Moudafi’s iterative algorithm
α-nonexpansive mapping

ASJC Scopus subject areas

General Mathematics

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10.1007/s12215-019-00418-z

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title = "Strong and ▵ -convergence of Moudafi{\textquoteright}s iterative algorithm for generalized nonexpansive mappings in convex metric spaces",

abstract = "We study Moudafi{\textquoteright}s iterative algorithm for an α-nonexpansive mapping and a fundamentally nonexpansive mapping in the framework of a convex metric space. We prove ▵-convergence and strong convergence results for the algorithm to a common fixed point of the mappings. Our results are new and are also valid in CAT(0) spaces and Banach spaces, simultaneously.",

keywords = "Common fixed point, Convergence, Convex metric space, Fundamentally nonexpansive mapping, Moudafi{\textquoteright}s iterative algorithm, α-nonexpansive mapping",

author = "Hafiz Fukhar-ud-din and Khan, \{Abdul Rahim\}",

note = "Publisher Copyright: {\textcopyright} 2019, Springer-Verlag Italia S.r.l., part of Springer Nature.",

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AU - Fukhar-ud-din, Hafiz

AU - Khan, Abdul Rahim

PY - 2020/8/1

Y1 - 2020/8/1

N2 - We study Moudafi’s iterative algorithm for an α-nonexpansive mapping and a fundamentally nonexpansive mapping in the framework of a convex metric space. We prove ▵-convergence and strong convergence results for the algorithm to a common fixed point of the mappings. Our results are new and are also valid in CAT(0) spaces and Banach spaces, simultaneously.

AB - We study Moudafi’s iterative algorithm for an α-nonexpansive mapping and a fundamentally nonexpansive mapping in the framework of a convex metric space. We prove ▵-convergence and strong convergence results for the algorithm to a common fixed point of the mappings. Our results are new and are also valid in CAT(0) spaces and Banach spaces, simultaneously.

KW - Common fixed point

KW - Convergence

KW - Convex metric space

KW - Fundamentally nonexpansive mapping

KW - Moudafi’s iterative algorithm

KW - α-nonexpansive mapping

UR - https://www.scopus.com/pages/publications/85065958243

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DO - 10.1007/s12215-019-00418-z

M3 - Article

AN - SCOPUS:85065958243

SN - 0009-725X

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EP - 559

JO - Rendiconti del Circolo Matematico di Palermo

JF - Rendiconti del Circolo Matematico di Palermo

IS - 2

ER -

Strong and ▵ -convergence of Moudafi’s iterative algorithm for generalized nonexpansive mappings in convex metric spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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