A five-step approximation method for a nonlinear delay integral equation in hyperbolic spaces: A qualitative study

In this manuscript, we design and present a Jungck-type iterative method to find the common fixed point of a pair of mappings with weak compatibility in hyperbolic metric spaces. Strong convergence is perfomed to estimate the common fixed point, and stability of the designed iterative scheme is established under suitable assumptions. Further, $\mathrm{\Delta }$-convergence is established, and a theoretical result is outlined to exhibit the coherence and effectiveness of our scheme with some of its counterparts. A numerical case study is set forth to evidence the convergence and effectiveness of the proposed method. Finally, the efficacy and applicability of our proposed method is illustrated by implementing it to explore a nonlinear delay integral equation (NDIE).