Abstract Let (E, F) be a nonempty pair subsets of a metric space (M, d) and let T: E ∪ F → E ∪ F T: E F E F be a noncyclic mapping, means that, T (E) ⊆ E, T (F) ⊆ F T (E) E, T (F) F. In this context, a point (x ⋆, y ⋆) ∈ E × F is called a best proximity pair for the mapping T T if d (x ⋆, y ⋆) = d i s t (E, F), T x ⋆ = x ⋆, T y ⋆ = y ⋆. d (x^, y^) =dist (E, F), Tx^ =x^, Ty^ =y^. In this article, in the setting of strictly convex hyperbolic metric spaces, we deal on the existence and convergence of best proximity pairs for the noncyclic version of the Reich’s contraction mapping T T which satisfies the following condition: d (T x, T y
Gabeleh et al. (Thu,) studied this question.