Geodesic
Some Remarks Concerning Contraction Mappings
Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 121-124

Voir la notice de l'article provenant de la source Cambridge University Press

The following result is proved in [1, p. 6].Theorem 1. Let X be a complete metric space, and let T and Tn(n = 1, 2,...)be contraction mappings of X into itself with the same Lipschitz constant k<1, and with fixed points u and un respectively. Suppose that limn → ∞ Tn(x) = T(x) for every x ∊ X. Then limn → ∞ un = u. 
Reich, Simeon. Some Remarks Concerning Contraction Mappings. Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 121-124. doi: 10.4153/CMB-1971-024-9
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