Convergence and Coupled Best Proximity Points: Ulam–Hyers Stability and an Application to a Two‐Person Game

ABSTRACT This paper aims to establish the uniqueness of a coupled best proximity point for cyclic Kannan contraction mappings in the setting of uniformly convex Banach spaces. The stability of the coupled best proximity point problem under the Ulam–Hyers framework is also studied. Since the existence of a noncooperative equilibrium is equivalent to the existence of a coupled fixed point, our results can be effectively applied to solve the problem of finding a noncooperative equilibrium in two‐person games. Furthermore, we present illustrative examples to support our findings.