Journal of Prime Research in Mathematics
Vol. 18 (2022), Issue 1, pp. 7 – 17
ISSN: 1817-3462E (Online) 1818-5495 (Print)
ISSN: 1817-3462E (Online) 1818-5495 (Print)
Fixed Point Approximations of a Family of
α-nonexpansive Mappings in CAT(0) Spaces
Sundus Shahzeen\(^{a,*}\), Maqbool Ahmed\(^a\), Liliana Guran\(^b\)
\(^a\) Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.
\(^b\) Vasile Goldis” Western University of Arad, Romania.
Correspondence should be addressed to: sundas_shahzeen@outlook.com
\(^a\) Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.
\(^b\) Vasile Goldis” Western University of Arad, Romania.
Correspondence should be addressed to: sundas_shahzeen@outlook.com
Copyright © 2022 Sundus Shahzeen, Maqbool Ahmed, Liliana Guran. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Published: Received: 3 January 2022; Accepted: 17 May 2022; Published Online: 7 June 2022.
Abstract
In this article, the results deal with the strong convergence of Halpern iteration in CAT(0) spaces. The study revolves around finding a fixed point for nonexpansive mappings, which are also the metric projection points in CA(0) space.Moreover, the strong convergence of Halpern iteration for α-nonexpansive mapping sequence is also given.Our results extend some known results which appeared in the literature.
Keywords:
CAT(0) space, Common Fixed Points, Halpern iteration, Semigroups.