Convergence of Iterative Scheme for Asymptotically Nonexpansive Mapping in Hadamard Spaces-Reference-Cited by-同舟云学术

Convergence of Iterative Scheme for Asymptotically Nonexpansive Mapping in Hadamard Spaces

Published:2022-12-22 Issue: Volume:22 Page:47-54
ISSN:2224-2880
Container-title:WSEAS TRANSACTIONS ON MATHEMATICS
language:en
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Author:

Padcharoen Anantachai¹,Sukprasert Pakeeta²

Affiliation:

1. Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University, Chanthaburi 22000, THAILAND

2. Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani 12110, THAILAND

Abstract

In this paper, we introduce and prove the convergence of a novel iterative scheme for asymptotically nonexpansive mapping under some suitable conditions in the context of Hadamard spaces. We also present a numerical experiment in which the rate of convergence of the new iterative scheme is compared to that of an existing iterative scheme.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

General Mathematics

Reference20 articles.

1. M. Bridson, A. Haefliger, Metric Spaces of NonPositive Curvature. Springer, Berlin 1999.

2. W.A. Kirk, Geodesic geometry and fixed point theory, In Seminar of Mathematical Analysis (Malaga/Seville, 2002/2003), pp. 195–225, Colecc. Abierta, 64, Univ. Sevilla Secr. Publ., Seville, 2003.

3. Y.I. Alber, C.E. Chidume, H. Zegeye, Approximating fixed points of total asymptotically nonexpansive mappings, Fixed Point Theory Appl., 10673 (2006).

4. W.R. Mann, Mean value methods in iteration,Proceedings of the American Mathematical Society, 4(3): 506, 1953.

5. S. Ishikawa, Fixed points by a new iteration method, Proceedings of the American Mathematical Society, 44(1): 147–150, 1974.