AK-iterative scheme for fixed point approximation in hyperbolic metric spaces and applications in Volterra integral equation

Abstract In this paper, we utilize the AK-iteration procedure for hyperbolic metric spaces, ensuring the symmetry condition is met and establish the weak w^2 w 2 -stability and data dependence results for contraction mappings. Additionally, we establish several Δ-convergence and strong convergence theorems for the generalized (, ) (α, β) -nonexpansive (GABNE) mappings. To demonstrate it, we provide a numerical example of the GABNE-mappings, emphasizing the enhanced efficiency of the AK-iteration method relative to other iterative approaches. Additionally, the applications of the main results are demonstrated by solving 2 D and 3 D Volterra integral equations. These findings extend and improve numerous related results found in the current literature.