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Universalium. 2010.
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
Brouwer fixed-point theorem — /brow euhr fikst poynt /, Math. the theorem that for any continuous transformation of a circle into itself, including its boundary, there is at least one point that is mapped to itself. [named after L. E. J. BROUWER] … Useful english dictionary
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
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
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
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
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
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
Fixed point theorems in infinite-dimensional spaces — In mathematics, a number of fixed point theorems in infinite dimensional spaces generalise the Brouwer fixed point theorem. They have applications, for example, to the proof of existence theorems for partial differential equations. The first… … Wikipedia
Fixed-point theorems in infinite-dimensional spaces — In mathematics, a number of fixed point theorems in infinite dimensional spaces generalise the Brouwer fixed point theorem. They have applications, for example, to the proof of existence theorems for partial differential equations. The first… … Wikipedia
