@article{Şahin2024, 
author = {Aynur Şahin and Zeynep Kalkan},
title = {The  AA-iterative algorithm in hyperbolic spaces with applications to integral equations on time scales},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {24480-24506},
keywords = {hyperbolic space, fixed point, generalized (α, β)-nonexpansive map, the AA-iterative algorithm, time scale, integral equations, weak w2-stability},
url = {https://www.sciopen.com/article/10.3934/math.20241192},
doi = {10.3934/math.20241192},
abstract = {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  (α,β)-nonexpansive ( GαβN) maps in such spaces. Through this algorithm, we derived compelling outcomes for both strong and  Δ-convergence and weak  w2-stability. Furthermore, we provided an illustrative example of  GαβN 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.}
}