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Research Article | Open Access

Computational comparative analysis of fixed point approximations of generalized α-nonexpansive mappings in hyperbolic spaces

Liliana Guran1,2, Khushdil Ahmad3, Khurram Shabbir3, Monica-Felicia Bota4( )
Department of Pharmaceutical Sciences, "Vasile Goldiş" Western University of Arad, Arad 310048, Romania
Department of Hospitality Services, Babeş-Bolyai University, Cluj-Napoca 400174, Romania
Department of Mathematics, Government College University, Lahore 54000, Pakistan
Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca 400084, Romania
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Abstract

In this article, we use the Picard-Thakur hybrid iterative scheme to approximate the fixed points of generalized α-nonexpansive mappings. For generalized α-nonexpansive mappings in hyperbolic spaces, we show several weak and strong convergence results. It is proved numerically and graphically that the Picard-Thakur hybrid iterative scheme converges more faster than other well-known hybrid iterative methods for generalized α-nonexpansive mappings. We also present an application to Fredholm integral equation.

Keywords

Picard-Thakur hybrid iterationgeneralized α-nonexpansive mappingfixed pointhyperbolic space
CLC number: 47H05, 47H10, 47J25

References

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AIMS Mathematics
Volume 8 Issue 2,
February 2023
Pages 2489-2507
DOI: 10.3934/math.2023129

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Cite this article:
Guran L, Ahmad K, Shabbir K, et al. Computational comparative analysis of fixed point approximations of generalized α-nonexpansive mappings in hyperbolic spaces. AIMS Mathematics, 2023, 8(2): 2489-2507. https://doi.org/10.3934/math.2023129

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Received: 02 September 2022
Revised: 25 October 2022
Accepted: 31 October 2022
Published: 15 February 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)