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Abstract
This paper introduces a novel class of generalized nonexpansive mapping in hyperbolic spaces. We employ a four-step iterative scheme to approximate the fixed points of this new class and establish strong convergence theorem for it. Using polynomiography, we visually compare the dynamical behavior of the four-step scheme against the Mann, Ishikawa, Noor, S-iteration, Picard-S, and Abbas iterations, and complement this with numerical experiments that consistently show faster convergence and reduced execution time. As an application, we use the four-step scheme to approximate solutions of a nonlinear Volterra integral equation in hyperbolic spaces, showcasing its versatility and potential for real-world applications.
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Kalsoom, A., Ashraf, P., Bibi, A. et al. Approximating fixed point of new generalized nonexpansive mapping. Sci Rep (2026). https://doi.org/10.1038/s41598-026-66523-z
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DOI: https://doi.org/10.1038/s41598-026-66523-z