Three-step iterative algorithm for a pair of total asymptotically nonexpansive mappings in uniformly convex metric spaces

Hafiz Fukhar-Ud-din; Safeer Hussain Khan

doi:10.2298/FIL1711573F

Three-step iterative algorithm for a pair of total asymptotically nonexpansive mappings in uniformly convex metric spaces

Hafiz Fukhar-Ud-din, Safeer Hussain Khan^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

Abstract

We introduce and study a three-step iterative algorithm for a pair of total asymptotically nonexpansive mappings in a uniformly convex metric space. The proposed algorithm includes Mann and Ishikawa iterative algorithms, the iterative algorithm of Khan and Takahashi [13] and the three-step iterative algorithm of Xu and Noor [26] as special cases. Our results are new and generalize several recent results in Hilbert spaces, uniformly convex Banach spaces and CAT (0) spaces, simultaneously.

Original language	English
Pages (from-to)	19-27
Number of pages	9
Journal	Filomat
Volume	31
Issue number	11
DOIs	https://doi.org/10.2298/FIL1711573F
State	Published - 2017

Bibliographical note

Publisher Copyright:
© 2017, University of Nis. All rights reserved.

Keywords

An iterative algorithm
Common fixed point
Convex metric space
Total asymptotically nonexpansive mapping
△-convergence and strong convergence

ASJC Scopus subject areas

General Mathematics

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10.2298/FIL1711573F

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abstract = "We introduce and study a three-step iterative algorithm for a pair of total asymptotically nonexpansive mappings in a uniformly convex metric space. The proposed algorithm includes Mann and Ishikawa iterative algorithms, the iterative algorithm of Khan and Takahashi [13] and the three-step iterative algorithm of Xu and Noor [26] as special cases. Our results are new and generalize several recent results in Hilbert spaces, uniformly convex Banach spaces and CAT (0) spaces, simultaneously.",

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AB - We introduce and study a three-step iterative algorithm for a pair of total asymptotically nonexpansive mappings in a uniformly convex metric space. The proposed algorithm includes Mann and Ishikawa iterative algorithms, the iterative algorithm of Khan and Takahashi [13] and the three-step iterative algorithm of Xu and Noor [26] as special cases. Our results are new and generalize several recent results in Hilbert spaces, uniformly convex Banach spaces and CAT (0) spaces, simultaneously.

KW - An iterative algorithm

KW - Common fixed point

KW - Convex metric space

KW - Total asymptotically nonexpansive mapping

KW - △-convergence and strong convergence

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Three-step iterative algorithm for a pair of total asymptotically nonexpansive mappings in uniformly convex metric spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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