Iterative algorithms for common fixed points of a countable family of quasi-nonexpansive multivalued mappings in CAT(0) spaces

In this paper, we propose an iterative scheme for a common fixed point of a countable family of quasi-nonexpansive mappings. The scheme is computationally less expensive, built on a geodesic averaging technique involving only selected elements. At each iteration, the scheme requires only geodesic segments and no further technical looping or optimizations. Under distinct mild conditions, we establish both \(\triangle\) $▵$ -convergence and strong convergence result for the proposed scheme to the required point, assuming existence. Notably, the considered mappings need not have compact images, among other relaxed conditions. Additionally, numerical experiments conducted show the robustness of the scheme. The results presented in this paper, not only enhances the existing related literature, but also offers valuable complements to previous studies.