A MIXED-TYPE PICARD-S ITERATIVE METHOD FOR ESTIMATING COMMON FIXED POINTS IN HYPERBOLIC SPACES

Austine Efut Ofem; Jacob Ashiwere Abuchu; Godwin Chidi Ugwunnadi; Ojen Kumar Narain; Hassen Aydi; Choonkil Park

doi:10.11948/20230125

2024 Volume 14 Issue 3

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Austine Efut Ofem, Jacob Ashiwere Abuchu, Godwin Chidi Ugwunnadi, Ojen Kumar Narain, Hassen Aydi, Choonkil Park. A MIXED-TYPE PICARD-S ITERATIVE METHOD FOR ESTIMATING COMMON FIXED POINTS IN HYPERBOLIC SPACES[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1302-1329. doi: 10.11948/20230125

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Austine Efut Ofem, Jacob Ashiwere Abuchu, Godwin Chidi Ugwunnadi, Ojen Kumar Narain, Hassen Aydi, Choonkil Park. A MIXED-TYPE PICARD-S ITERATIVE METHOD FOR ESTIMATING COMMON FIXED POINTS IN HYPERBOLIC SPACES[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1302-1329. doi: 10.11948/20230125

A MIXED-TYPE PICARD-S ITERATIVE METHOD FOR ESTIMATING COMMON FIXED POINTS IN HYPERBOLIC SPACES

1.
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
2.
Department of Mathematics, University of Calabar, Calabar, Nigeria
3.
Department of Mathematics, University of Eswatini, Kwaluseni, Eswatini
4.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94 Medunsa 0204, Pretoria, South Africa
5.
Université de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
6.
China Medical Univesity Hospital, China Medical University, Taichung 40402, Taiwan
7.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa
8.
Research Institute for Convergence of Basic Science, Hanyang University, Seoul 04763, Korea

Author Bio: Email: 222128007@stu.ukzn.ac.za(A. E. Ofem); Email: 221114675@stu.ukzn.ac.za(J. A. Abuchu); Email: ugwunnadi4u@yahoo.com(G. C. Ugwunnadi); Email: naraino@ukzn.ac.za(O. K. Narain)
Corresponding authors: Email: hassen.aydi@isima.rnu.tn(H. Aydi); Email: baak@hanyang.ac.kr(C. Park)

Abstract

Abstract

This article presents a modified Picard-S iterative method in hyperbolic spaces. The proposed iterative method is used to approximate the common fixed point of two contractive-like mappings. We consider new concepts of data dependence and weak $ w^2 $-stability results of the proposed iterative scheme involving two contractive-like mappings in hyperbolic spaces. We prove the strong and $ \triangle $-convergence results of our new algorithm for common fixed points of two mappings enriched with the condition $ (E) $. With numerical examples, we show the advantage and efficiency of the proposed method over some existing methods. Our results generalize and improve several results in the literature.
- Weak $w^2$-stability /
- data dependence /
- strong and $\vartriangle$-convergence /
- common fixed point
MSC: 47H05, 47H09, 39B82

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References

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