A fixed point theorem for multivalued mappings with $$\delta$$-distance.(English)Zbl 1469.54033

Summary: 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 $$\delta : B(X) \times B(X) \rightarrow \mathbb{R}$$ 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 $$T : X \rightarrow B(X)$$ is a multivalued certain contraction, then $$T$$ has a fixed point.

MSC:

 54H25 Fixed-point and coincidence theorems (topological aspects) 54C60 Set-valued maps in general topology 54E40 Special maps on metric spaces 54E50 Complete metric spaces
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References:

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