The existence of best proximity points for multivalued non-self-mappings (Q380422)

In this paper, the authors present sufficient conditions which ensure the existence of best proximity points for multivalued non-self-mappings. Let \(A, B\) be nonempty subsets of a metric space \((X, d)\) and \(T : A \to 2^B\) be a multivalued non-self-mapping. A best proximity point for \(T\) is a point \(x^{*} \in A\) which satisfies \(\inf \{d(x^* , y) : y \in Tx^*\} = \operatorname{dist}(A, B)\). For contraction multivalued non-self-mappings in metric spaces, as well as for nonexpansive multivalued non-self-mappings in Banach spaces having an appropriate geometric property, the authors prove sufficient conditions which ensure the existence of best proximity points.