A Fixed Point Theorem for Multivalued Mappings withδ-Distance

Abstract

We mainly study fixed point theorem for multivalued mappings withδ-distance using Wardowski’s technique on complete metric space. Let(X,d)be a metric space and letB(X)be a family of all nonempty bounded subsets ofX. Defineδ:B(X)×B(X)→Rbyδ(A,B)=supd(a,b):a∈A,b∈B.Consideringδ-distance, it is proved that if(X,d)is a complete metric space andT:X→B(X)is a multivalued certain contraction, thenThas a fixed point.