Computational comparative analysis of fixed point approximations of generalized $ \alpha $-nonexpansive mappings in hyperbolic spaces

Liliana Guran; Khushdil Ahmad; Khurram Shabbir; Monica-Felicia Bota; Liliana Guran; Khushdil Ahmad; Khurram Shabbir; Monica-Felicia Bota

doi:10.3934/math.2023129

AIMS Mathematics

2023, Volume 8, Issue 2: 2489-2507. doi: 10.3934/math.2023129

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Computational comparative analysis of fixed point approximations of generalized $ \alpha $-nonexpansive mappings in hyperbolic spaces

1.
Department of Pharmaceutical Sciences, "Vasile Goldiş" Western University of Arad, Arad 310048, Romania
2.
Department of Hospitality Services, Babeş-Bolyai University, Cluj-Napoca 400174, Romania
3.
Department of Mathematics, Government College University, Lahore 54000, Pakistan
4.
Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca 400084, Romania

Received: 02 September 2022 Revised: 25 October 2022 Accepted: 31 October 2022 Published: 07 November 2022
MSC : 47H05, 47H10, 47J25

In this article, we use the Picard-Thakur hybrid iterative scheme to approximate the fixed points of generalized $ \alpha $-nonexpansive mappings. For generalized $ \alpha $-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 $ \alpha $-nonexpansive mappings. We also present an application to Fredholm integral equation.
- Picard-Thakur hybrid iteration,
- generalized $ \alpha $-nonexpansive mapping,
- fixed point,
- hyperbolic space
Citation: Liliana Guran, Khushdil Ahmad, Khurram Shabbir, Monica-Felicia Bota. Computational comparative analysis of fixed point approximations of generalized $ \alpha $-nonexpansive mappings in hyperbolic spaces[J]. AIMS Mathematics, 2023, 8(2): 2489-2507. doi: 10.3934/math.2023129

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Abstract

In this article, we use the Picard-Thakur hybrid iterative scheme to approximate the fixed points of generalized $ \alpha $-nonexpansive mappings. For generalized $ \alpha $-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 $ \alpha $-nonexpansive mappings. We also present an application to Fredholm integral equation.

References

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