A Fixed Point Theorem for Multivalued Mappings with delta-Distance

Abstract

We mainly study fixed point theorem for multivalued mappings with delta-distance using Wardowski's technique on complete metric space. Let (X, d) be a metric space and let B(X) be a family of all nonempty bounded subsets of X. Define delta : B(X) x B(X) -> R by delta(A, B) = sup {d(a, b): a is an element of A, b is an element of B}. Considering delta-distance, it is proved that if (X, d) is a complete metric space and T : X -> B(X) is a multivalued certain contraction, then T has a fixed point.