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...

Discrete fixed-point theorems were developed by Iimura, Murota and Tamura, Chen and Deng and others. Yang provides a survey. Continuous fixed-point theorems...

Brouwer fixed-point theorem: that is, f {\displaystyle f} is continuous and maps the unit d-cube to itself. The Brouwer fixed-point theorem guarantees...

neutrally stable fixed point. Multiple attracting points can be collected in an attracting fixed set. The Banach fixed-point theorem gives a sufficient...

In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate...

the Jordan curve theorem is equivalent to the strong Hex theorem, which is a purely discrete theorem. The Brouwer fixed point theorem, by being sandwiched...

Helly's theorem is a basic result in discrete geometry on the intersection of convex sets. It was discovered by Eduard Helly in 1913, but not published...

result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent to it. It states that every Sperner coloring...

Bernoulli process Digital data Discrete calculus Discrete system Discretization Normalized frequency Nyquist–Shannon sampling theorem Time-scale calculus "Digital...

Arrow's impossibility theorem is a key result in social choice theory showing that no ranked-choice procedure for group decision-making can satisfy the...

any point must be a finite group (alternatively, the point is the only system allowing for infinite rotational symmetry). The strength of the theorem is...

with entropy H(X) in the discrete-valued case and differential entropy in the continuous-valued case. The Source coding theorem states that for any ε >...

whose systole is larger or equal than any fixed ε > 0 {\displaystyle \varepsilon >0} . Mahler's compactness theorem was generalized to semisimple Lie groups...

Hausdorff maximality theorem (set theory) Kleene fixed-point theorem (order theory) Knaster–Tarski theorem (order theory) Kruskal's tree theorem (order theory)...

only finitely many fixed points, is either a fixed point, a periodic orbit, or a connected set composed of a finite number of fixed points together with...

fixed-point theorem proves that a solution can be obtained by fixed-point iteration of successive approximations. In this context, this fixed-point iteration...

equivalent to the Brouwer fixed-point theorem.: 545  It is sometimes called the Miranda theorem or the Bolzano–Poincaré–Miranda theorem. The picture on the...

central limit theorem applies in particular to sums of independent and identically distributed discrete random variables. A sum of discrete random variables...

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have...

remain useful, Bayes' theorem can be formulated in terms of the relevant densities (see Derivation). If X is continuous and Y is discrete, f X | Y = y ( x...

There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information...

Two Squares Theorem", Discrete Mathematics, 339 (2016) 1410–1411. Two more proofs at PlanetMath.org "A one-sentence proof of the theorem". Archived from...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

Roberts's triangle theorem, a result in discrete geometry, states that every arrangement of n {\displaystyle n} lines, with no parallel lines and no crossings...

(the images of a given point under all group elements) forms a discrete set. All finite symmetry groups are discrete. Discrete symmetry groups come in...

explicit proofs, so this theorem is sometimes known as the Lüders–Pauli theorem. At about the same time, and independently, this theorem was also proved by...

Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic...

Conley's fundamental theorem of dynamical systems or Conley's decomposition theorem states that every flow of a dynamical system with compact phase portrait...

Journal on Discrete Mathematics, 30 (2): 1102–1114, doi:10.1137/15M105149X, MR 3504983 Deza, Michel; Frankl, Péter (1983), "Erdős–Ko–Rado theorem – 22 years...

Kirchberger's theorem is a theorem in discrete geometry, on linear separability. The two-dimensional version of the theorem states that, if a finite set...