AK-iterative scheme for fixed point approximation in hyperbolic metric spaces and applications in Volterra integral equation
Abstract
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 $(\alpha ,\beta )$ ( 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.
Fields of Study & Subjects
Fixed Point Theorems Analysis
Optimization and Variational Analysis
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Fixed Point Theory and Algorithms for Sciences and Engineering
- Publisher
- Springer Science and Business Media LLC
- Volume
- 2026
- Issue
- 1
- Publication date
- 7 January 2026
- Language
- EN