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Mathematics 2017, 5(1), 14; doi:10.3390/math5010014

A Novel Iterative Algorithm Applied to Totally Asymptotically Nonexpansive Mappings in CAT(0) Spaces

Department of Mathemathics, Imam Khomeini International University, Qazvin 34149, Iran
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Academic Editor: Lokenath Debnath
Received: 31 December 2016 / Revised: 12 February 2017 / Accepted: 16 February 2017 / Published: 22 February 2017
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Abstract

In this paper we introduce a new iterative algorithm for approximating fixed points of totally asymptotically quasi-nonexpansive mappings on CAT(0) spaces. We prove a strong convergence theorem under suitable conditions. The result we obtain improves and extends several recent results stated by many others; they also complement many known recent results in the literature. We then provide some numerical examples to illustrate our main result and to display the efficiency of the proposed algorithm. View Full-Text
Keywords: iterative algorithm; totally asymptotically quasi-nonexpansive mapping; ▵-convergence; CAT(0) space iterative algorithm; totally asymptotically quasi-nonexpansive mapping; ▵-convergence; CAT(0) space
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Abkar, A.; Shekarbaigi, M. A Novel Iterative Algorithm Applied to Totally Asymptotically Nonexpansive Mappings in CAT(0) Spaces. Mathematics 2017, 5, 14.

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