The $AA$-iterative algorithm in hyperbolic spaces with applications to integral equations on time scales

We explored the $AA$-iterative algorithm within the hyperbolic spaces (HSs), aiming to unveil a stability outcome for contraction maps and convergence outcomes for generalized $(\alpha ,\beta )$-nonexpansive ( $G\alpha \beta N$) maps in such spaces. Through this algorithm, we derived compelling outcomes for both strong and $\mathrm{\Delta }$-convergence and weak $w^2$-stability. Furthermore, we provided an illustrative example of $G\alpha \beta N$ maps and conducted a comparative analysis of convergence rates against alternative iterative methods. Additionally, we demonstrated the practical relevance of our findings by applying them to solve the linear Fredholm integral equations (FIEs) and nonlinear Fredholm-Hammerstein integral equations (FHIEs) on time scales.