Extended Ulam–Hyers stability results in Hadamard spaces: Best proximity approach

In this paper, we develop existence theorems for coupled best proximity points of (Formula presented.) -cyclic contraction mappings as well as (Formula presented.) -cyclic nonexpansive mappings. We also establish Ulam–Hyers stability of the corresponding best proximity point problems in the setting of Hadamard spaces and Busemann convex spaces. Moreover, we introduce the notion of the coupled HW property and, based on this concept, establish a new result on the existence of coupled best proximity points for (Formula presented.) -cyclic contractions.