Some Remarks on “On Enriched Suzuki Mappings in Hadamard Spaces” [Mathematics 2024, 12(1), 157]

In this paper, we critically examine the work of Turcanu and Postolache [29], identifying several results that appear to be mathematically incorrect. To substantiate our claims, we provide a counterexample and propose corrected versions of the results. Furthermore, we develop new existence and convergence theorems for approximating fixed points of a class of Suzuki b -enriched nonexpansive mappings. Our analysis is conducted within the framework of geodesic spaces, employing the Krasnosel’skiĭ iterative method. Finally, we obtain a fixed point convergence theorem for enriched Suzuki nonexpansive mappings in complete CAT ₚ(0) p ( 0 ) spaces by employing the concept of the nearest point projection.