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#banach_fixed-point_theorem

Banach fixed-point theorem

Theorem about metric spaces

In mathematics, the Banach fixed-point theorem is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces and provides a constructive method to find those fixed points. It can be understood as an abstract formulation of Picard's method of successive approximations. The theorem is named after Stefan Banach (1892–1945) who first stated it in 1922.

Mon 16th

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Banach fixed-point theorem Fixed-point theorem Fixed-point iteration Stefan Banach Schauder fixed-point theorem Picard–Lindelöf theorem Brouwer fixed-point theorem Fixed point (mathematics) Fixed-point theorems in infinite-dimensional spaces Caristi fixed-point theorem
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