Convergence analysis of modified iterative approaches in geodesic spaces with curvature bounded above

The objective of this article is to establish a new modified iteration process for nonexpansive mappings in complete CAT(κ) spaces. We prove strong and Δ‐convergence theorems of the proposed method in such spaces under some standard conditions. Furthermore, numerical experiments of non‐trivial examples are also provided to show performance and comparison speed of convergence with many previously known methods. Our main result extended and improved the corresponding recent results announced by many researchers.