Some results on Best proximity in geodesic spaces

Eldred and Veeramani have proved the existence and uniqueness of best proximity for contraction cyclic contraction mapping in uniformly convex banach spaces. In this paper, Eldred and Veeramani study is extended to geodesic spaces particularly in CAT(0) spaces, prove the sequences ( x 2 n ) and (x 2 n +1) are Cauchy sequences and prove the existenace and uniqueness of best proximity point for contraction cyclic mapping in CAT(0) spaces.