Geodesic
A Note on an Iterative Test of Edelstein(1)
Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 381-386

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Let (X1, d1) and (X2, d2) be metric spaces. A mapping/: X1→X2 is said to be a Lipschitz mapping (with respect to d1 and d2) if and only if (*)d2(f(x), f(y))≤λ⋅ d1(x, y) for all x, y∈X1, where λ is a fixed real number. The constant λ is called a Lipschitz constant for f. If (*) is satisfied for λ=l, then f is called nonexpansive (see, for example, [21]) and if (*), again with λ=1, is replaced by a strict inequality for all x≠y, then f is called contractive [1]. If x∊X1 and X1=X2, then the sequence where f 1(x)=f(x) and f n(x)=f(f n-1(x)) for each n>1, is called the sequence of iterates of f at x. 
Jr., Sam B. Nadler. A Note on an Iterative Test of Edelstein(1). Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 381-386. doi: 10.4153/CMB-1972-070-7
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     title = {A {Note} on an {Iterative} {Test} of {Edelstein(1)}},
     journal = {Canadian mathematical bulletin},
     pages = {381--386},
     year = {1972},
     volume = {15},
     number = {3},
     doi = {10.4153/CMB-1972-070-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-070-7/}
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