A best approximation theorem in hyperconvex metric spaces

In this paper, we present a best approximation theorem for set-valued mappings in hyperconvex metric spaces, which generalize the well-known result of Kirk, Sims and Yuan [W.A. Kirk, B. Sims, X.Z. Yuan, The Knaster–Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications, Nonlinear Anal. 39 (2000) 611–627].