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

Tehreem Ishtiaq; Afshan Batool; Aftab Hussain; Hamed Alsulami

doi:10.3390/axioms14120889

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Article

30 November 2025

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

and

Department of Mathematical Sciences, Fatima Jinnah Women University, Rawalpindi 46000, Pakistan

Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

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Axioms2025, 14(12), 889;https://doi.org/10.3390/axioms14120889
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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

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