fixed-point theorem
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Fixed point theorem — In mathematics, a fixed point theorem is a result saying that a function F will have at least one fixed point (a point x for which F ( x ) = x ), under some conditions on F that can be stated in general terms. Results of this kind are amongst the … Wikipedia
fixed-point theorem — ▪ mathematics any of various theorems in mathematics dealing with a transformation of the points of a set into points of the same set where it can be proved that at least one point remains fixed. For example, if each real number is squared … Universalium
Kakutani fixed point theorem — In mathematical analysis, the Kakutani fixed point theorem is a fixed point theorem for set valued functions. It provides sufficient conditions for a set valued function defined on a convex, compact subset of a Euclidean space to have a fixed… … Wikipedia
Brouwer fixed point theorem — In mathematics, the Brouwer fixed point theorem is an important fixed point theorem that applies to finite dimensional spaces and which forms the basis for several general fixed point theorems. It is named after Dutch mathematician L. E. J.… … Wikipedia
Banach fixed-point theorem — In mathematics, the Banach fixed point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of… … Wikipedia
Banach fixed point theorem — The Banach fixed point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self maps… … Wikipedia
Lefschetz fixed-point theorem — In mathematics, the Lefschetz fixed point theorem is a formula that counts the number of fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X . It … Wikipedia
Atiyah–Bott fixed-point theorem — In mathematics, the Atiyah–Bott fixed point theorem, proven by Michael Atiyah and Raoul Bott in the 1960s, is a general form of the Lefschetz fixed point theorem for smooth manifolds M , which uses an elliptic complex on M . This is a system of… … Wikipedia
Caristi fixed point theorem — In mathematics, the Caristi fixed point theorem (also known as the Caristi Kirk fixed point theorem) generalizes the Banach fixed point theorem for maps of a complete metric space into itself. Caristi s fixed point theorem is a variation of the… … Wikipedia
Brouwer's fixed point theorem — ▪ topology in mathematics, a theorem of algebraic topology (topology) that was stated and proved in 1912 by the Dutch mathematician L.E.J. Brouwer (Brouwer, Luitzen Egbertus Jan). Inspired by earlier work of the French mathematician Henri… … Universalium
Schauder fixed point theorem — The Schauder fixed point theorem is an extension of the Brouwer fixed point theorem to topological vector spaces such as Banach spaces. It asserts that if K is a compact, convex subset of a topological vector space and T is a continuous mapping… … Wikipedia
