Abstract

We consider two nonempty subsets $\mathcal{A}$ and $\mathcal{B}$ be of a hyperbolic space $(\bar{X}, d, \mathcal{W})$ and $T: \mathcal{A} \rightarrow 2^{\mathcal{B}}$ is a multivalued nonself-mapping. We establish a existence theorem for a best proximity pair $\bar{x}$ such that $d(\bar{x},T\bar{x})=d(\mathcal{A},\mathcal{B})=\inf\{d(x,y): x\in \mathcal{A}, y\in \mathcal{B}\}$.

Keywords and Phrases

Best proximity pair, hyperbolic spaces, proximinal retract.

A.M.S. subject classification

47H09, 47H10.

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