A fixed point theorem for multivalued mappings with δ -Distance

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.