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Longer titles found: Fixed-point theorems in infinite-dimensional spaces (view), Kakutani fixed-point theorem (view), Brouwer fixed-point theorem (view), Banach fixed-point theorem (view), Schauder fixed-point theorem (view), Lefschetz fixed-point theorem (view), Kleene fixed-point theorem (view), Atiyah–Bott fixed-point theorem (view), Caristi fixed-point theorem (view), Earle–Hamilton fixed-point theorem (view), Ryll-Nardzewski fixed-point theorem (view), Borel fixed-point theorem (view), Markov–Kakutani fixed-point theorem (view), Browder fixed-point theorem (view), Discrete fixed-point theorem (view), Lawvere's fixed-point theorem (view)

searching for Fixed-point theorem 75 found (481 total)

alternate case: fixed-point theorem

Euler's rotation theorem (4,497 words) [view diff] no match in snippet view article find links to article

In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains
Holomorphic Lefschetz fixed-point formula (157 words) [view diff] no match in snippet view article find links to article
In mathematics, the Holomorphic Lefschetz formula is an analogue for complex manifolds of the Lefschetz fixed-point formula that relates a sum over the
Elliptic complex (267 words) [view diff] no match in snippet view article find links to article
connection with the Atiyah-Singer index theorem and Atiyah-Bott fixed point theorem. If E0, E1, ..., Ek are vector bundles on a smooth manifold M (usually
Witt's theorem (564 words) [view diff] no match in snippet view article find links to article
theorem" or "the Witt theorem" may also refer to the Bourbaki–Witt fixed point theorem of order theory. In mathematics, Witt's theorem, named after Ernst
Barycentric subdivision (2,533 words) [view diff] exact match in snippet view article find links to article
maps on those of simplicial maps, as for instance in Lefschetz's fixed-point theorem. The Lefschetz number is a useful tool to find out whether a continuous
Continuous game (2,007 words) [view diff] no match in snippet view article find links to article
guaranteed; this is by Glicksberg's generalization of the Kakutani fixed point theorem. The class of continuous games is for this reason usually defined
Lie–Kolchin theorem (528 words) [view diff] no match in snippet view article find links to article
algebraic groups was proved by Ellis Kolchin (1948, p.19). The Borel fixed point theorem generalizes the Lie–Kolchin theorem. Sometimes the theorem is also
William Arthur Kirk (215 words) [view diff] no match in snippet view article find links to article
for example, he is one of the two namesakes of the Caristi-Kirk fixed point theorem of 1976. He is also known for the Kirk theorem of 1964. He completed
Diagonal lemma (1,745 words) [view diff] no match in snippet view article find links to article
lemma (also known as diagonalization lemma, self-reference lemma or fixed point theorem) establishes the existence of self-referential sentences in certain
Victor Lomonosov (270 words) [view diff] no match in snippet view article find links to article
theorem". Lomonosov gives a very short proof, using the Schauder fixed point theorem, that if a bounded linear operator T on a Banach space commutes with
Oliver Dimon Kellogg (441 words) [view diff] no match in snippet view article find links to article
Theory. In 1922 with George David Birkhoff he generalized the Brouwer fixed point theorem to the theorem of Birkhoff–Kellogg. Among his doctoral students was
Degree of a continuous mapping (1,906 words) [view diff] no match in snippet view article find links to article
the degree is homotopy invariant and used it to prove the Brouwer fixed point theorem. Less general forms of the concept existed before Brouwer, such as
Maximal compact subgroup (1,772 words) [view diff] no match in snippet view article find links to article
a semisimple Lie group uniqueness is a consequence of the Cartan fixed point theorem, which asserts that if a compact group acts by isometries on a complete
Triangulation (topology) (5,150 words) [view diff] exact match in snippet view article
continuous maps on those of simplicial maps, for instance in Lefschetz's fixed-point theorem. The Lefschetz number is a useful tool to find out whether a continuous
Czesław Ryll-Nardzewski (488 words) [view diff] no match in snippet view article find links to article
probability theory. Several theorems bear his name: the Ryll-Nardzewski fixed point theorem, the Ryll-Nardzewski theorem in model theory, and the Kuratowski
Initial value problem (1,377 words) [view diff] no match in snippet view article find links to article
such that the solution is a fixed point of the operator. The Banach fixed point theorem is then invoked to show that there exists a unique fixed point, which
Lowell E. Jones (337 words) [view diff] exact match in snippet view article find links to article
Hsiang. Jones' dissertation topic, assigned by Hsiang, concerned the fixed-point theorem of Paul Althaus Smith. Jones joined Stony Brook University in 1975
Direction-preserving function (1,465 words) [view diff] no match in snippet view article find links to article
6)\cdot f^{c}(2,7)=-1<0} . Iimura, Takuya (2003-09-01). "A discrete fixed point theorem and its applications". Journal of Mathematical Economics. 39 (7):
Helmut H. Schaefer (540 words) [view diff] no match in snippet view article find links to article
Leipzig Known for Work on topological vector spaces, Schaefer's fixed point theorem Scientific career Institutions University of Halle University of
Graph equation (273 words) [view diff] no match in snippet view article find links to article
Discrete Mathematics, 1975 Graph equations, graph inequalities and a fixed point theorem, DM Cvetkovic, IB Lackovic, SK Simic – Publ. Inst. Math.(Belgrade)
Alexander Doniphan Wallace (748 words) [view diff] exact match in snippet view article find links to article
1090/s0002-9904-1945-08416-x. MR 0013302. Wallace, A. D. (1945). "A fixed-point theorem". Bulletin of the American Mathematical Society. 51, Part 1 (6):
Samuel Eilenberg (812 words) [view diff] no match in snippet view article find links to article
Press. MR 0050886. Stefan Banach Stanislaw Ulam Eilenberg–Montgomery fixed point theorem "Samuel Eilenberg - Biography". Maths History. Retrieved 2024-07-26
Schröder–Bernstein theorem (2,374 words) [view diff] no match in snippet view article find links to article
Schröder–Bernstein theorem. There is also a proof which uses Tarski's fixed point theorem. Myhill isomorphism theorem Netto's theorem, according to which the
Conley–Zehnder theorem (187 words) [view diff] no match in snippet view article find links to article
several others. Conley, C. C.; Zehnder, E. (1983), "The Birkhoff–Lewis fixed point theorem and a conjecture of V. I. Arnol'd" (PDF), Inventiones Mathematicae
Eilenberg–Steenrod axioms (750 words) [view diff] no match in snippet view article find links to article
a retract of the n-disk. This is used in a proof of the Brouwer fixed point theorem. A "homology-like" theory satisfying all of the Eilenberg–Steenrod
Mizar system (1,225 words) [view diff] no match in snippet view article find links to article
examples are the Hahn–Banach theorem, Kőnig's lemma, the Brouwer fixed point theorem, Gödel's completeness theorem, and the Jordan curve theorem. This
David Gale (851 words) [view diff] exact match in snippet view article find links to article
Mathematical Monthly 81(1974), pp. 876–879. The game of Hex and the Brouwer fixed-point theorem. American Mathematical Monthly 86(1979), pp. 818–827. The strategy
Jacques Tits (985 words) [view diff] no match in snippet view article find links to article
cone Tits group Tits index Tits metric Tits systems Bruhat–Tits fixed point theorem Freudenthal–Tits magic square Kantor–Koecher–Tits construction Artin-Tits
Carathéodory metric (621 words) [view diff] no match in snippet view article find links to article
show that α(x, v) ≥ ||v||, with equality when x = 0. Earle–Hamilton fixed point theorem Earle, Clifford J. and Harris, Lawrence A. and Hubbard, John H. and
Subindependence (320 words) [view diff] no match in snippet view article find links to article
doi:10.1198/tast.2009.09051. Hamedani, G.G.; Walter, G.G. (1984). "A fixed point theorem and its application to the central limit theorem". Archiv der Mathematik
Oscar Lanford (1,030 words) [view diff] no match in snippet view article find links to article
Tresser. Lanford later gave a shorter proof using the Leray-Schauder fixed point theorem but establishing only the fixed point without the hyperbolicity.
Invariant convex cone (3,569 words) [view diff] exact match in snippet view article find links to article
Brouwer fixed-point theorem can be avoided by applying more direct fixed-point theorems for holomorphic mappings, such as the Earle–Hamilton fixed point theorem
Circle packing theorem (3,857 words) [view diff] no match in snippet view article find links to article
topological proofs that are known. Thurston's proof is based on Brouwer's fixed point theorem. As a graduate student, Oded Schramm was supervised by Thurston at
Lionel W. McKenzie (650 words) [view diff] no match in snippet view article find links to article
proof of the existence of a general equilibrium, using Kakutani's fixed point theorem. Another proof, by Kenneth Arrow and Gérard Debreu, was published
Paul C. Rosenbloom (599 words) [view diff] no match in snippet view article find links to article
1090/s0002-9939-1973-0312303-3. MR 0312303. Rosenbloom, P. C. (1973). "A fixed point theorem for mappings in scaled metric spaces, with applications to partial
Andrew Browder (562 words) [view diff] no match in snippet view article find links to article
article "Topology in the Complex Plane", which described the Brouwer fixed point theorem, the Jordan curve theorem, and Alexander duality. With Hiroshi Yamaguchi
Integrally convex set (556 words) [view diff] no match in snippet view article find links to article
Takuya; Murota, Kazuo; Tamura, Akihisa (2005-12-01). "Discrete fixed point theorem reconsidered" (PDF). Journal of Mathematical Economics. 41 (8): 1030–1036
List of real analysis topics (1,603 words) [view diff] no match in snippet view article find links to article
polynomials Legendre polynomials Euclidean space Metric space Banach fixed point theorem – guarantees the existence and uniqueness of fixed points of certain
Proof theory (2,669 words) [view diff] exact match in snippet view article find links to article
second incompleteness theorem). There are also modal analogues of the fixed-point theorem. Robert Solovay proved that the modal logic GL is complete with respect
Euler's Gem (934 words) [view diff] no match in snippet view article find links to article
characteristic of Seifert surfaces, the Poincaré–Hopf theorem, the Brouwer fixed point theorem, Betti numbers, and Grigori Perelman's proof of the Poincaré conjecture
Eduard Zehnder (608 words) [view diff] no match in snippet view article find links to article
no. 4, 539–603. C.C. Conley and E. Zehnder. The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnolʹd. Invent. Math. 73 (1983), no. 1
Mu-Tao Wang (759 words) [view diff] no match in snippet view article find links to article
mass–energy; the Wang-Yau quasi-local mass is named in his honor. "A fixed point theorem of isometry action on Riemannian manifolds", Journal of Differential
Catamorphism (1,835 words) [view diff] no match in snippet view article find links to article
types, which, however, can be united by the isomorphism from the fixed point theorem. We introduce the term zero, which arises from Maybe's Nothing and
Dan McKenzie (geophysicist) (1,398 words) [view diff] no match in snippet view article
published a seminal paper with Bob Parker, which employed Euler's Fixed Point Theorem, in conjunction with magnetic anomalies and earthquakes to determine
Quine (computing) (2,564 words) [view diff] no match in snippet view article
JavaScript Machine, with a series of interactive hints A Java Quine built straight from Kleene's fixed point theorem, composition and s-n-m A QR code quine
Stochastic matrix (2,959 words) [view diff] no match in snippet view article find links to article
absolute value of all its eigenvalues is also 1. Finally, the Brouwer Fixed Point Theorem (applied to the compact convex set of all probability distributions
Axiom (4,918 words) [view diff] no match in snippet view article find links to article
Mendelson, "3. First-Order Theories" of Ch. 2 Mendelson, "5. The Fixed Point Theorem. Gödel's Incompleteness Theorem" of Ch. 2 Mendelson, Elliot (1987)
Closure operator (2,656 words) [view diff] no match in snippet view article find links to article
J(lim T) = lim J(T). This continuity condition is on the basis of a fixed point theorem for J. Consider the one-step operator J of a monotone logic. This
Simplicial homology (2,141 words) [view diff] no match in snippet view article find links to article
is essential to applications of the theory, including the Brouwer fixed point theorem and the topological invariance of simplicial homology. Singular homology
Hausdorff dimension (3,145 words) [view diff] no match in snippet view article find links to article
_{i}(A).} The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets
Ivar Ekeland (2,261 words) [view diff] no match in snippet view article find links to article
space. Ekeland's principle leads to a quick proof of the Caristi fixed point theorem. Ekeland was associated with the University of Paris when he proposed
Erich Rothe (1,598 words) [view diff] no match in snippet view article find links to article
Fréchet derivative is a completely continuous operator and for Rothe's fixed point theorem, proven in 1937. In 1978 a collection of papers was published in
Thurston boundary (1,393 words) [view diff] no match in snippet view article find links to article
isotopy class of the identity). The proof relies on the Brouwer fixed point theorem applied to the action of ϕ {\displaystyle \phi } on the Thurston
Zorn's lemma (4,674 words) [view diff] exact match in snippet view article find links to article
(sometimes named Tukey's lemma) Bourbaki–Witt theorem – a choiceless fixed-point theorem that can be combined with choice to prove Zorn's lemma Serre, Jean-Pierre
Tsachik Gelander (676 words) [view diff] no match in snippet view article find links to article
S2CID 14172846. Bader, U.; Gelander, T.; Monod, N. (27 October 2011). "A fixed point theorem for L 1 spaces". Inventiones Mathematicae. 189 (1). Springer Science
Abstract economy (3,378 words) [view diff] no match in snippet view article find links to article
semi-continuous] is lower semi-continuous. The proofs use the Kakutani fixed point theorem. An exchange economy is a system with N-1 consumers and l {\displaystyle
Reverse mathematics (4,782 words) [view diff] no match in snippet view article find links to article
function on the closed unit interval is Riemann integrable. The Brouwer fixed point theorem (for continuous functions on an n {\displaystyle n} -simplex).Theorem
Fractal (8,399 words) [view diff] no match in snippet view article find links to article
turbulence data. Mathematics portal Systems science portal Banach fixed point theorem – Theorem about metric spacesPages displaying short descriptions
Combinatory logic (5,301 words) [view diff] no match in snippet view article find links to article
x) then B else A) ≡ λx.((N x) B A) Define ABSURDUM ≡ (Y NEGATION) Fixed point theorem gives: ABSURDUM = (NEGATION ABSURDUM), for ABSURDUM ≡ (Y NEGATION)
Alfred Tarski (5,757 words) [view diff] exact match in snippet view article find links to article
of model theory Logic of relations Banach–Tarski paradox Tarski's fixed-point theorem Tarski-style universes Tarski's axioms Tarski monster group Tarski's
Louis Nirenberg (5,007 words) [view diff] no match in snippet view article find links to article
Math. 17 (1964), 101–134. Fan, Ky. A generalization of Tychonoff's fixed point theorem. Math. Ann. 142 (1960), 305–310. Fan, Ky. A minimax inequality and
List of victims of Nazism (265 words) [view diff] no match in snippet view article find links to article
by the Gestapo, Warsaw Juliusz Schauder 1899–1943 Polish Schauder fixed point theorem, Schauder basis Jewish executed by the Gestapo, Lviv Włodzimierz
List of victims of Nazism (265 words) [view diff] no match in snippet view article find links to article
by the Gestapo, Warsaw Juliusz Schauder 1899–1943 Polish Schauder fixed point theorem, Schauder basis Jewish executed by the Gestapo, Lviv Włodzimierz
Anders Karlsson (mathematician) (631 words) [view diff] no match in snippet view article
Learn. Res. 23, 1, Article 191. Anders Karlsson (2024). "A Metric Fixed Point Theorem and Some of Its Applications". Geom. Funct. Anal. 34, 486–511. (DOI:
Equidissection (3,532 words) [view diff] case mismatch in snippet view article find links to article
has media related to Equidissections. Sperner’s Lemma, Brouwer’s Fixed-Point Theorem, And The Subdivision Of Squares Into Triangles - Notes by Akhil Mathew
Brouwer–Hilbert controversy (4,395 words) [view diff] exact match in snippet view article find links to article
he had published a number of important papers, in particular the fixed-point theorem. Hilbert admired Brouwer and helped him receive a regular academic
Complex hyperbolic space (2,077 words) [view diff] no match in snippet view article find links to article
}^{n}\cup \partial \mathbb {H} _{\mathbb {C} }^{n}} . By Brouwer's fixed point theorem, any holomorphic isometry of the complex hyperbolic space must fix
List of University of Kansas people (5,579 words) [view diff] exact match in snippet view article find links to article
tampon Solomon Lefschetz (1884–1972), known for his topological fixed-point theorem Stanley Lombardo, classics professor and translator of classical
Möbius transformation (10,603 words) [view diff] exact match in snippet view article find links to article
of the circle (real projective line) is 0, and thus the Lefschetz fixed-point theorem says only that it must fix at least 0 points, but possibly more.
Rotation matrix (15,809 words) [view diff] no match in snippet view article find links to article
November 2021. Palais, Bob; Palais, Richard (2007-12-20). "Euler's fixed point theorem: The axis of a rotation". Journal of Fixed Point Theory and Applications
Market design (4,191 words) [view diff] no match in snippet view article find links to article
of stable matchings was reminiscent of the conclusion of Tarski's fixed point theorem, which states that an increasing function from a complete lattice
Homotopy groups of spheres (8,126 words) [view diff] no match in snippet view article find links to article
polynomial has a zero. The fact that πn−1(Sn−1) = Z implies the Brouwer fixed point theorem that every continuous map from the n-dimensional ball to itself has
Perron–Frobenius theorem (8,225 words) [view diff] no match in snippet view article find links to article
point-set topology. A common thread in many proofs is the Brouwer fixed point theorem. Another popular method is that of Wielandt (1950). He used the Collatz–Wielandt
Constructive set theory (35,229 words) [view diff] no match in snippet view article find links to article
to the Brouwer fixed point theorem and other theorems regarding values of continuous functions on the reals. The fixed point theorem in turn implies
Common fixed point problem (2,015 words) [view diff] no match in snippet view article find links to article
1090/S0002-9939-1964-0184217-8. DeMarr, Ralph (1963). "A common fixed point theorem for commuting mappings". The American Mathematical Monthly. 70 (5):