Geodesic
A Note on Lipschitzian Mappings in Convex Metric Spaces
Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 463-466

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Local criteria are given which imply the lipschitzian character of mappings defined in complete and convex metric spaces. 
Kirk, W. A.; Ray, WIlliam O. A Note on Lipschitzian Mappings in Convex Metric Spaces. Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 463-466. doi: 10.4153/CMB-1977-068-6
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[1] 1. Clarke, F., Pointwise contraction criteria for the existence of fixed points, preprint. Google Scholar

[2] 2. Kirk, W.A. and Ray, W.O., A remark on directional contractions, Proc. Amer. Math. Soc. (to appear). Google Scholar

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