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

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 w²-stability results of the proposed iterative scheme involving two contractive-like mappings in hyperbolic spaces. We prove the strong and Δ-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.

Original language	English
Pages (from-to)	1302-1329
Number of pages	28
Journal	Journal of Applied Analysis and Computation
Volume	14
Issue number	3
DOIs	https://doi.org/10.11948/20230125
Publication status	Published - Jun 2024
Externally published	Yes

Keywords

Weak w-stability
common fixed point
data dependence
strong and Δ-convergence

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10.11948/20230125

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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 w2-stability results of the proposed iterative scheme involving two contractive-like mappings in hyperbolic spaces. We prove the strong and Δ-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.",

keywords = "Weak w-stability, common fixed point, data dependence, strong and Δ-convergence",

author = "Ofem, {Austine Efut} and Abuchu, {Jacob Ashiwere} and Ugwunnadi, {Godwin Chidi} and Narain, {Ojen Kumar} and Hassen Aydi and Choonkil Park",

year = "2024",

month = jun,

doi = "10.11948/20230125",

language = "English",

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AU - Ofem, Austine Efut

AU - Abuchu, Jacob Ashiwere

AU - Ugwunnadi, Godwin Chidi

AU - Narain, Ojen Kumar

AU - Aydi, Hassen

AU - Park, Choonkil

PY - 2024/6

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N2 - 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 w2-stability results of the proposed iterative scheme involving two contractive-like mappings in hyperbolic spaces. We prove the strong and Δ-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.

AB - 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 w2-stability results of the proposed iterative scheme involving two contractive-like mappings in hyperbolic spaces. We prove the strong and Δ-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.

KW - Weak w-stability

KW - common fixed point

KW - data dependence

KW - strong and Δ-convergence

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

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Keywords

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