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Volume 14
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Article

Common Fixed Point Approximation for Asymptotically Nonexpansive Mapping in Hyperbolic Space with Application

by
Tehreem Ishtiaq
1,
Afshan Batool
1,
Aftab Hussain
2,* and
Hamed Alsulami
2
1
Department of Mathematical Sciences, Fatima Jinnah Women University, Rawalpindi 46000, Pakistan
2
Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(12), 889; https://doi.org/10.3390/axioms14120889
Submission received: 14 October 2025 / Revised: 23 November 2025 / Accepted: 26 November 2025 / Published: 30 November 2025
(This article belongs to the Special Issue Recent Advances in Special Functions and Applications, 2nd Edition)
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Abstract

This study presents a common fixed-point iteration process that includes two asymptotically nonexpansive self-mappings in a hyperbolic space and their delta convergence. To support our results, we provide an example with a comparison table and sufficient conditions for a modified iteration scheme to have strong convergence to approximate the fixed point.
Keywords: modified iteration; common fixed point; nonexpansive mapping; convergence; hyperbolic space modified iteration; common fixed point; nonexpansive mapping; convergence; hyperbolic space

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MDPI and ACS Style

Ishtiaq, T.; Batool, A.; Hussain, A.; Alsulami, H. Common Fixed Point Approximation for Asymptotically Nonexpansive Mapping in Hyperbolic Space with Application. Axioms 2025, 14, 889. https://doi.org/10.3390/axioms14120889

AMA Style

Ishtiaq T, Batool A, Hussain A, Alsulami H. Common Fixed Point Approximation for Asymptotically Nonexpansive Mapping in Hyperbolic Space with Application. Axioms. 2025; 14(12):889. https://doi.org/10.3390/axioms14120889

Chicago/Turabian Style

Ishtiaq, Tehreem, Afshan Batool, Aftab Hussain, and Hamed Alsulami. 2025. "Common Fixed Point Approximation for Asymptotically Nonexpansive Mapping in Hyperbolic Space with Application" Axioms 14, no. 12: 889. https://doi.org/10.3390/axioms14120889

APA Style

Ishtiaq, T., Batool, A., Hussain, A., & Alsulami, H. (2025). Common Fixed Point Approximation for Asymptotically Nonexpansive Mapping in Hyperbolic Space with Application. Axioms, 14(12), 889. https://doi.org/10.3390/axioms14120889

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