A Fixed Point Theorem for Multivalued Mappings with δ -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 $\delta :B(X)\times B(X)\to \mathbb{R}$ by $\delta (A,B)=\text{sup}\left\{d(a,b):a\in A,b\in B\right\}.$ Considering $\delta$-distance, it is proved that if $(X,d)$ is a complete metric space and $T:X\to B(X)$ is a multivalued certain contraction, then $T$ has a fixed point.