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On uniformly Lipschitzian multivalued mappings in Banach and metric spaces. (English) Zbl 1218.47077
The authors introduce the concept of uniformly k-Lipschitzian multivalued mapping and prove a fixed point result for this kind of mappings in complete CAT(0) spaces, under the condition that the Lipschitz constant is strictly less than 2. Other results for these mappings are given in p-uniformly convex metric spaces and in complete metric spaces, in this last case under the condition that the Lipschitz constant is strictly less than the Lifšic constant of the space.
MSC:
47H09Mappings defined by “shrinking” properties
47H10Fixed point theorems for nonlinear operators on topological linear spaces
54H25Fixed-point and coincidence theorems in topological spaces
54E50Complete metric spaces