A Fixed Point Theorem for Multivalued Mappings with δ -Distance

Abstract EN

We mainly study fixed point theorem for multivalued mappings with δ -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 δ : B ( X ) × B ( X ) → R by δ ( A , B ) = sup d ( a , b ) : a ∈ A , b ∈ B .

Considering δ -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.