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

Hafiz Fukhar-Ud-din; Safeer H 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 H Khan

Mathematics and Statistics

King Fahd University of Petroleum and Minerals
Islamia University
Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University

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 - Jan 1 2017

Keywords

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

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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.

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KW - Total asymptotically nonexpansive mapping

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

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