Uniformly contractive fixed points in compact metric spaces

Leader, Solomon

doi:10.1090/S0002-9939-1982-0663887-2

Uniformly contractive fixed points in compact metric spaces
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by Solomon Leader

Proc. Amer. Math. Soc. 86 (1982), 153-158

DOI: https://doi.org/10.1090/S0002-9939-1982-0663887-2

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Abstract:

Let $f$ be a continuous self-map on a compact metric space. Equivalent conditions are given for the existence of a uniformly contractive fixed point $w({f^n}x \to w$ uniformly for all $x$). Corollaries give sufficient conditions for uniformly contractive fixed points subsuming some known results.

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