Geodesic
The Fixed Point Set of Real Multi-Valued Contraction Mappings
Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 507-511

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Let (X, d1) and (Y, d2) be metric spaces. A mapping f:X→Y is said to be a Lipschitz mapping if there exists a real number λ such that for each x,y∊X. We call λ a Lipschitz constant for f. If λ∊[0, 1), f is called a contraction mapping. Throughout this note CB(Y) denotes the set of closed and bounded subsets of Y equipped with the Hausdorff metric induced by d2. 
Finbow, Arthur S. The Fixed Point Set of Real Multi-Valued Contraction Mappings. Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 507-511. doi: 10.4153/CMB-1972-089-9
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