The Brouwer Fixed Point Theorem. - Duke Mathematics Department The Brouwer Fixed Point Theorem. Fix a positive integer n and let Dn = fx 2 Rn: jxj • 1g. Our goal is to prove The Brouwer Fixed Point Theorem. Suppose f: Dn! Dn is continuous. Then f has a fixed point; that is, there is a 2 Dn such that f(a) = a. This wil
Fixed-point theorem - Wikipedia, the free encyclopedia 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 ...
Brouwer fixed-point theorem - Wikipedia, the free encyclopedia Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f mapping a compact ...
Lefschetz fixed-point theorem - Wikipedia, the free encyclopedia In mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space X to itself ...
Kleene fixed-point theorem - Wikipedia, the free encyclopedia In the mathematical areas of order and lattice theory, the Kleene fixed-point theorem, named after American mathematician Stephen Cole Kleene, states the ...
Schauder fixed point theorem - Wikipedia, the free encyclopedia The Schauder fixed point theorem is an extension of the Brouwer fixed point theorem to topological vector spaces, which may be of infinite dimension. It asserts ...
Knaster–Tarski theorem - Wikipedia, the free encyclopedia [edit]. Since complete lattices cannot be empty, the theorem in particular guarantees the existence of ...
Kakutani fixed-point theorem - Wikipedia, the free encyclopedia 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 ...
Borel fixed-point theorem - Wikipedia, the free encyclopedia In mathematics, the Borel fixed-point theorem is a fixed-point theorem in algebraic geometry generalizing the Lie-Kolchin theorem. The result was proved by ...
Fixed Point Theorem -- from Wolfram MathWorld Fixed Point Theorem. If g is a continuous function g(x) in [a,b] for all x in [a,b] , then g has a fixed point in [a,b] . This can be proven by supposing that ...
