I came across the statement ``Every closed and convex subset of a uniformly convex b-metric space is Chebychev'' in [1]. Here, the term `convex' is in the sense of Takahashi. I tried looking up for the proof of the same without success. I would be grateful if someone can direct me to the proof. Thanks.

[1] H. Fukhar-ud-din, One step iterative scheme for a pair of nonexpansive mappings in a convex metric space, Hacet. J. Math. Stat., Vol. 44 (2015), 1023 – 1031.