Numerical analysis demonstrates superior convergence speed using a four-step iterative scheme in hyperbolic spaces, highlighting its utility for solving nonlinear integral equations.
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 et al. (2026) studied this question.
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