Banach's fixed-point theorem

Banach's fixed-point theorem

[¦bä‚näks ‚fikst ‚pȯint ′thir·əm] (mathematics) A theorem stating that if a mapping ƒ of a metric space E into itself is a contraction, then there exists a unique element x of E such that ƒ x = x. Also known as Caccioppoli-Banach principle.