# Category: Inequalities

Bernoulli's inequality
In mathematics, Bernoulli's inequality (named after Jacob Bernoulli) is an inequality that approximates exponentiations of 1 + x. It is often employed in real analysis. It has several useful variants:
No description available.
Gibbs' inequality
In information theory, Gibbs' inequality is a statement about the information entropy of a discrete probability distribution. Several other bounds on the entropy of probability distributions are deriv
Kraft–McMillan inequality
In coding theory, the Kraft–McMillan inequality gives a necessary and sufficient condition for the existence of a prefix code (in Leon G. Kraft's version) or a uniquely decodable code (in Brockway McM
HM-GM-AM-QM inequalities
In mathematics, the HM-GM-AM-QM inequalities state the relationship between the harmonic mean, geometric mean, arithmetic mean, and quadratic mean (aka root mean square or RMS for short). Suppose that
Newton's inequalities
In mathematics, the Newton inequalities are named after Isaac Newton. Suppose a1, a2, ..., an are real numbers and let denote the kth elementary symmetric polynomial in a1, a2, ..., an. Then the eleme
Bell's theorem
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories given some basic
Lebedev–Milin inequality
In mathematics, the Lebedev–Milin inequality is any of several inequalities for the coefficients of the exponential of a power series, found by Lebedev and Milin and Isaak Moiseevich Milin. It was use
In mathematics, Hadamard's inequality (also known as Hadamard's theorem on determinants) is a result first published by Jacques Hadamard in 1893. It is a bound on the determinant of a matrix whose ent
Fekete–Szegő inequality
In mathematics, the Fekete–Szegő inequality is an inequality for the coefficients of univalent analytic functions found by Fekete and Szegő, related to the Bieberbach conjecture. Finding similar estim
Tupper's self-referential formula
Tupper's self-referential formula is a formula that visually represents itself when graphed at a specific location in the (x, y) plane.
Lieb–Thirring inequality
In mathematics and physics, Lieb–Thirring inequalities provide an upper bound on the sums of powers of the negative eigenvalues of a Schrödinger operator in terms of integrals of the potential. They a
Turán–Kubilius inequality
The Turán–Kubilius inequality is a mathematical theorem in probabilistic number theory. It is useful for proving results about the normal order of an arithmetic function. The theorem was proved in a s
Singleton bound
In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude upper bound on the size of an arbitrary block code with block length , size and minimum distance . It
Kantorovich inequality
In mathematics, the Kantorovich inequality is a particular case of the Cauchy–Schwarz inequality, which is itself a generalization of the triangle inequality. The triangle inequality states that the l
Maclaurin's inequality
In mathematics, Maclaurin's inequality, named after Colin Maclaurin, is a refinement of the inequality of arithmetic and geometric means. Let a1, a2, ..., an be positive real numbers, and for k = 1, 2
Poincaré inequality
In mathematics, the Poincaré inequality is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincaré. The inequality allows one to obtain bounds on a function using
Inequalities in information theory
Inequalities are very important in the study of information theory. There are a number of different contexts in which these inequalities appear.
Brezis–Gallouet inequality
In mathematical analysis, the Brezis–Gallouët inequality, named after Haïm Brezis and Thierry Gallouët, is an inequality valid in 2 spatial dimensions. It shows that a function of two variables which
Karamata's inequality
In mathematics, Karamata's inequality, named after Jovan Karamata, also known as the majorization inequality, is a theorem in elementary algebra for convex and concave real-valued functions, defined o
Mahler's inequality
In mathematics, Mahler's inequality, named after Kurt Mahler, states that the geometric mean of the term-by-term sum of two finite sequences of positive numbers is greater than or equal to the sum of
Chebyshev–Markov–Stieltjes inequalities
In mathematical analysis, the Chebyshev–Markov–Stieltjes inequalities are inequalities related to the problem of moments that were formulated in the 1880s by Pafnuty Chebyshev and proved independently
Weierstrass product inequality
In mathematics, the Weierstrass product inequality states that for any real numbers 0 ≤ a1, ..., an ≤ 1 we have where The inequality is named after the German mathematician Karl Weierstrass. It can be
FKG inequality
In mathematics, the Fortuin–Kasteleyn–Ginibre (FKG) inequality is a correlation inequality, a fundamental tool in statistical mechanics and probabilistic combinatorics (especially random graphs and th
List of inequalities
Popoviciu's inequality
In convex analysis, Popoviciu's inequality is an inequality about convex functions. It is similar to Jensen's inequality and was found in 1965 by Tiberiu Popoviciu, a Romanian mathematician.
Young's convolution inequality
In mathematics, Young's convolution inequality is a mathematical inequality about the convolution of two functions, named after William Henry Young.
Ingleton's inequality
In mathematics, Ingleton's inequality is an inequality that is satisfied by the rank function of any representable matroid. In this sense it is a necessary condition for representability of a matroid
Riesz rearrangement inequality
In mathematics, the Riesz rearrangement inequality, sometimes called Riesz–Sobolev inequality, states that any three non-negative functions , and satisfy the inequality where , and are the symmetric d
Cohn-Vossen's inequality
In differential geometry, Cohn-Vossen's inequality, named after Stefan Cohn-Vossen, relates the integral of Gaussian curvature of a non-compact surface to the Euler characteristic. It is akin to the G
Correlation inequality
A correlation inequality is any of a number of inequalities satisfied by the correlation functions of a model. Such inequalities are of particular use in statistical mechanics and in percolation theor
Rearrangement inequality
In mathematics, the rearrangement inequality states that for every choice of real numbersand every permutationof If the numbers are different, meaning that then the lower bound is attained only for th
Z-channel (information theory)
In coding theory and information theory, a Z-channel (binary asymmetric channel) is a communications channel used to model the behaviour of some data storage systems.
Bessel's inequality
In mathematics, especially functional analysis, Bessel's inequality is a statement about the coefficients of an element in a Hilbert space with respect to an orthonormal sequence. The inequality was d
Clarkson's inequalities
In mathematics, Clarkson's inequalities, named after James A. Clarkson, are results in the theory of Lp spaces. They give bounds for the Lp-norms of the sum and difference of two measurable functions
Ky Fan inequality
In mathematics, there are two different results that share the common name of the Ky Fan inequality. One is an inequality involving the geometric mean and arithmetic mean of two sets of real numbers o
Sobolev inequality
In mathematics, there is in mathematical analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces. These are used to prove the Sobolev embedding theorem, giving inclu
Weyl's inequality (number theory)
In number theory, Weyl's inequality, named for Hermann Weyl, states that if M, N, a and q are integers, with a and q coprime, q > 0, and f is a real polynomial of degree k whose leading coefficient c
Wirtinger's inequality for functions
In mathematics, historically Wirtinger's inequality for real functions was an inequality used in Fourier analysis. It was named after Wilhelm Wirtinger. It was used in 1904 to prove the isoperimetric
Peetre's inequality
In mathematics, Peetre's inequality, named after Jaak Peetre, says that for any real number t and any vectors x and y in Rn, the following inequality holds:
Morse inequalities
No description available.
In mathematics, Ladyzhenskaya's inequality is any of a number of related functional inequalities named after the Soviet Russian mathematician Olga Aleksandrovna Ladyzhenskaya. The original such inequa
Schur test
In mathematical analysis, the Schur test, named after German mathematician Issai Schur, is a bound on the operator norm of an integral operator in terms of its (see Schwartz kernel theorem). Here is o
Inequality of arithmetic and geometric means
In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal
Von Neumann's inequality
In operator theory, von Neumann's inequality, due to John von Neumann, states that, for a fixed contraction T, the polynomial functional calculus map is itself a contraction.
Young's inequality for products
In mathematics, Young's inequality for products is a mathematical inequality about the product of two numbers. The inequality is named after William Henry Young and should not be confused with Young's
Fischer's inequality
In mathematics, Fischer's inequality gives an upper bound for the determinant of a positive-semidefinite matrix whose entries are complex numbers in terms of the determinants of its principal diagonal
In mathematics, the Hermite–Hadamard inequality, named after Charles Hermite and Jacques Hadamard and sometimes also called Hadamard's inequality, states that if a function ƒ : [a, b] → R is convex, t
Leggett–Garg inequality
The Leggett–Garg inequality, named for Anthony James Leggett and Anupam Garg, is a mathematical inequality fulfilled by all macrorealistic physical theories. Here, macrorealism (macroscopic realism) i
Stein–Strömberg theorem
In mathematics, the Stein–Strömberg theorem or Stein–Strömberg inequality is a result in measure theory concerning the Hardy–Littlewood maximal operator. The result is foundational in the study of the
Fannes–Audenaert inequality
The Fannes–Audenaert inequality is a mathematical bound on the difference between the von Neumann entropies of two density matrices as a function of their trace distance. It was proved by Koenraad M.
Poincaré separation theorem
In mathematics, the Poincaré separation theorem gives the upper and lower bounds of eigenvalues of a real symmetric matrix B'AB that can be considered as the orthogonal projection of a larger real sym
Leggett inequality
The Leggett inequalities, named for Anthony James Leggett, who derived them, are a related pair of mathematical expressions concerning the correlations of properties of entangled particles. (As publis
Jensen's inequality
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by J
Landau–Kolmogorov inequality
In mathematics, the Landau–Kolmogorov inequality, named after Edmund Landau and Andrey Kolmogorov, is the following family of interpolation inequalities between different derivatives of a function f d
Lieb–Oxford inequality
In quantum chemistry and physics, the Lieb–Oxford inequality provides a lower bound for the indirect part of the Coulomb energy of a quantum mechanical system. It is named after Elliott H. Lieb and .
Nesbitt's inequality
In mathematics, Nesbitt's inequality states that for positive real numbers a, b and c, It is an elementary special case (N = 3) of the difficult and much studied Shapiro inequality, and was published
Steffensen's inequality
Steffensen's inequality is an equation in mathematics named after Johan Frederik Steffensen. It is an integral inequality in real analysis, stating: If ƒ : [a, b] → R is a non-negative, monotonically
Welch bounds
In mathematics, Welch bounds are a family of inequalities pertinent to the problem of evenly spreading a set of unit vectors in a vector space. The bounds are important tools in the design and analysi
Korn's inequality
In mathematical analysis, Korn's inequality is an inequality concerning the gradient of a vector field that generalizes the following classical theorem: if the gradient of a vector field is skew-symme
Carleman's inequality
Carleman's inequality is an inequality in mathematics, named after Torsten Carleman, who proved it in 1923 and used it to prove the Denjoy–Carleman theorem on quasi-analytic classes.
Łojasiewicz inequality
In real algebraic geometry, the Łojasiewicz inequality, named after Stanisław Łojasiewicz, gives an upper bound for the distance of a point to the nearest zero of a given real analytic function. Speci
CHSH inequality
In physics, the CHSH inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement in quantum mechanics can not be reproduced by local hidden-variable t
Gagliardo–Nirenberg interpolation inequality
In mathematics, and in particular in mathematical analysis, the Gagliardo–Nirenberg interpolation inequality is a result in the theory of Sobolev spaces that relates the -norms of different weak deriv
Schur's inequality
In mathematics, Schur's inequality, named after Issai Schur,establishes that for all non-negative real numbersx, y, z and t, with equality if and only if x = y = z or two of them are equal and the oth
Oscillatory integral operator
In mathematics, in the field of harmonic analysis, an oscillatory integral operator is an integral operator of the form where the function S(x,y) is called the phase of the operator and the function a
Hilbert's inequality
In analysis, a branch of mathematics, Hilbert's inequality states that for any sequence u1,u2,... of complex numbers. It was first demonstrated by David Hilbert with the constant 2π instead of π; the
Babenko–Beckner inequality
In mathematics, the Babenko–Beckner inequality (after K. Ivan Babenko and William E. Beckner) is a sharpened form of the Hausdorff–Young inequality having applications to uncertainty principles in the
Harnack's inequality
In mathematics, Harnack's inequality is an inequality relating the values of a positive harmonic function at two points, introduced by A. Harnack. Harnack's inequality is used to prove Harnack's theor
Generalized mean
In mathematics, generalized means (or power mean or Hölder mean from Otto Hölder) are a family of functions for aggregating sets of numbers. These include as special cases the Pythagorean means (arith
Shearer's inequality
Shearer's inequality or also Shearer's lemma, in mathematics, is an inequality in information theory relating the entropy of a set of variables to the entropies of a collection of subsets. It is named
XYZ inequality
In combinatorial mathematics, the XYZ inequality, also called the Fishburn–Shepp inequality, is an inequality for the number of linear extensions of finite partial orders. The inequality was conjectur
Three spheres inequality
In mathematics, the three spheres inequality bounds the norm of a harmonic function on a given sphere in terms of the norm of this function on two spheres, one with bigger radius and one with smaller
Pisier–Ringrose inequality
In mathematics, Pisier–Ringrose inequality is an inequality in the theory of C*-algebras which was proved by Gilles Pisier in 1978 affirming a conjecture of John Ringrose. It is an extension of the Gr
Hanner's inequalities
In mathematics, Hanner's inequalities are results in the theory of Lp spaces. Their proof was published in 1956 by Olof Hanner. They provide a simpler way of proving the uniform convexity of Lp spaces
Hausdorff–Young inequality
The Hausdorff−Young inequality is a foundational result in the mathematical field of Fourier analysis. As a statement about Fourier series, it was discovered by William Henry Young and extended by Hau
Markov brothers' inequality
In mathematics, the Markov brothers' inequality is an inequality proved in the 1890s by brothers Andrey Markov and Vladimir Markov, two Russian mathematicians. This inequality bounds the maximum of th
Littlewood's 4/3 inequality
In mathematical analysis, Littlewood's 4/3 inequality, named after John Edensor Littlewood, is an inequality that holds for every complex-valued bilinear form defined on c0, the Banach space of scalar
In mathematics, the Askey–Gasper inequality is an inequality for Jacobi polynomials proved by Richard Askey and George Gasper and used in the proof of the Bieberbach conjecture.
Schur-convex function
In mathematics, a Schur-convex function, also known as S-convex, isotonic function and order-preserving function is a function that for all such that is majorized by , one has that . Named after Issai
Log sum inequality
The log sum inequality is used for proving theorems in information theory.
In mathematics, Muirhead's inequality, named after Robert Franklin Muirhead, also known as the "bunching" method, generalizes the inequality of arithmetic and geometric means.
Stechkin's lemma
In mathematics – more specifically, in functional analysis and numerical analysis – Stechkin's lemma is a result about the ℓq norm of the tail of a sequence, when the whole sequence is known to have f
Fatou's lemma
In mathematics, Fatou's lemma establishes an inequality relating the Lebesgue integral of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions. The lemma
Interpolation inequality
In the field of mathematical analysis, an interpolation inequality is an inequality of the form where for , is an element of some particular vector space equipped with norm and is some real exponent,
Agmon's inequality
In mathematical analysis, Agmon's inequalities, named after Shmuel Agmon, consist of two closely related interpolation inequalities between the Lebesgue space and the Sobolev spaces . It is useful in
Less-than sign
The less-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the left, <, has been fou
Jordan's inequality
In mathematics, Jordan's inequality, named after Camille Jordan, states that It can be proven through the geometry of circles (see drawing).
Abel's inequality
In mathematics, Abel's inequality, named after Niels Henrik Abel, supplies a simple bound on the absolute value of the inner product of two vectors in an important special case.
Hardy's inequality
Hardy's inequality is an inequality in mathematics, named after G. H. Hardy. It states that if is a sequence of non-negative real numbers, then for every real number p > 1 one has If the right-hand si
Kallman–Rota inequality
In mathematics, the Kallman–Rota inequality, introduced by , is a generalization of the Landau–Kolmogorov inequality to Banach spaces. It states that if A is the infinitesimal generator of a one-param
Strichartz estimate
In mathematical analysis, Strichartz estimates are a family of inequalities for linear dispersive partial differential equations. These inequalities establish size and decay of solutions in Lebesgue s
Noether inequality
In mathematics, the Noether inequality, named after Max Noether, is a property of compact minimal complex surfaces that restricts the topological type of the underlying topological 4-manifold. It hold
Christ–Kiselev maximal inequality
In mathematics, the Christ–Kiselev maximal inequality is a maximal inequality for filtrations, named for mathematicians Michael Christ and Alexander Kiselev.
Ahlswede–Daykin inequality
The Ahlswede–Daykin inequality, also known as the four functions theorem (or inequality), is a correlation-type inequality for four functions on a finite distributive lattice. It is a fundamental tool
Hölder's inequality
In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of Lp spaces. Theorem (Hölder's inequality
Uncertainty principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with w
Hardy–Littlewood inequality
In mathematical analysis, the Hardy–Littlewood inequality, named after G. H. Hardy and John Edensor Littlewood, states that if and are nonnegative measurable real functions vanishing at infinity that
In complex analysis, a branch of mathematics, theHadamard three-circle theorem is a result about the behavior of holomorphic functions. Let be a holomorphic function on the annulus Let be the maximum
Trudinger's theorem
In mathematical analysis, Trudinger's theorem or the Trudinger inequality (also sometimes called the Moser–Trudinger inequality) is a result of functional analysis on Sobolev spaces. It is named after
Friedrichs's inequality
In mathematics, Friedrichs's inequality is a theorem of functional analysis, due to Kurt Friedrichs. It places a bound on the Lp norm of a function using Lp bounds on the weak derivatives of the funct
Inequality (mathematics)
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by
Jackson's inequality
In approximation theory, Jackson's inequality is an inequality bounding the value of function's best approximation by algebraic or trigonometric polynomials in terms of the modulus of continuity or mo
Grothendieck inequality
In mathematics, the Grothendieck inequality states that there is a universal constant with the following property. If Mij is an n × n (real or complex) matrix with for all (real or complex) numbers si
Chebyshev's sum inequality
In mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, states that if and then Similarly, if and then
Crossing number inequality
In the mathematics of graph drawing, the crossing number inequality or crossing lemma gives a lower bound on the minimum number of crossings of a given graph, as a function of the number of edges and
Denjoy–Koksma inequality
In mathematics, the Denjoy–Koksma inequality, introduced by , p.73) as a combination of work of Arnaud Denjoy and the Koksma–Hlawka inequality of Jurjen Ferdinand Koksma, is a bound for Weyl sums of f
Jørgensen's inequality
In the mathematical theory of Kleinian groups, Jørgensen's inequality is an inequality involving the traces of elements of a Kleinian group, proved by Troels Jørgensen. The inequality states that if A
Shapiro inequality
In mathematics, the Shapiro inequality is an inequality proposed by Harold S. Shapiro in 1954.
Erdős–Turán inequality
In mathematics, the Erdős–Turán inequality bounds the distance between a probability measure on the circle and the Lebesgue measure, in terms of Fourier coefficients. It was proved by Paul Erdős and P
Cauchy–Schwarz inequality
The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is considered one of the most important and widely used inequalities in mathematics. The inequality for sums was publi
Gregory coefficients
Gregory coefficients Gn, also known as reciprocal logarithmic numbers, Bernoulli numbers of the second kind, or Cauchy numbers of the first kind, are the rational numbers that occur in the Maclaurin s
Gårding's inequality
In mathematics, Gårding's inequality is a result that gives a lower bound for the bilinear form induced by a real linear elliptic partial differential operator. The inequality is named after Lars Gård
Sedrakyan's inequality
The following inequality is known as Sedrakyan's inequality, Bergström's inequality, Engel's form or Titu's lemma, respectively, referring to the article About the applications of one useful inequalit
Turán's inequalities
In mathematics, Turán's inequalities are some inequalities for Legendre polynomials found by Pál Turán (and first published by ). There are many generalizations to other polynomials, often called Turá
Van der Corput lemma (harmonic analysis)
In mathematics, in the field of harmonic analysis,the van der Corput lemma is an estimate for oscillatory integralsnamed after the Dutch mathematician J. G. van der Corput. The following result is sta
Wirtinger inequality (2-forms)
In mathematics, the Wirtinger inequality for 2-forms, named after Wilhelm Wirtinger, states that on a Kähler manifold M, the exterior kth power of the symplectic form (Kähler form) ω, when evaluated o
Mashreghi–Ransford inequality
In Mathematics, the Mashreghi–Ransford inequality is a bound on the growth rate of certain sequences. It is named after J. Mashreghi and T. Ransford. Let be a sequence of complex numbers, and let and
Cotlar–Stein lemma
In mathematics, in the field of functional analysis, the Cotlar–Stein almost orthogonality lemma is named after mathematicians Mischa Cotlarand Elias Stein. It may be used to obtain information on the
Levinson's inequality
In mathematics, Levinson's inequality is the following inequality, due to Norman Levinson, involving positive numbers. Let and let be a given function having a third derivative on the range , and such
Entropic uncertainty
In quantum mechanics, information theory, and Fourier analysis, the entropic uncertainty or Hirschman uncertainty is defined as the sum of the temporal and spectral Shannon entropies. It turns out tha
Dittert conjecture
The Dittert conjecture, or Dittert–Hajek conjecture, is a mathematical hypothesis (in combinatorics) concerning the maximum achieved by a particular function of matrices with real, nonnegative entries
Greater-than sign
The greater-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the right, >, has been
Minkowski inequality
In mathematical analysis, the Minkowski inequality establishes that the Lp spaces are normed vector spaces. Let S be a measure space, let 1 ≤ p < ∞ and let f and g be elements of Lp(S). Then f + g is
Bogomolov–Miyaoka–Yau inequality
In mathematics, the Bogomolov–Miyaoka–Yau inequality is the inequality between Chern numbers of compact complex surfaces of general type. Its major interest is the way it restricts the possible topolo
Bonse's inequality
In number theory, Bonse's inequality, named after H. Bonse, relates the size of a primorial to the smallest prime that does not appear in its prime factorization. It states that if p1, ..., pn, pn+1 a
Bihari–LaSalle inequality
The Bihari–LaSalle inequality, was proved by the American mathematicianJoseph P. LaSalle (1916–1983) in 1949 and by the Hungarian mathematicianImre Bihari (1915–1998) in 1956. It is the following nonl
Trace inequality
In mathematics, there are many kinds of inequalities involving matrices and linear operators on Hilbert spaces. This article covers some important operator inequalities connected with traces of matric
Saint-Venant's theorem
In solid mechanics, it is common to analyze the properties of beams with constant cross section. Saint-Venant's theorem states that the simply connected cross section with maximal torsional rigidity i
Aristarchus's inequality
Aristarchus's inequality (after the Greek astronomer and mathematician Aristarchus of Samos; c. 310 – c. 230 BCE) is a law of trigonometry which states that if α and β are acute angles (i.e. between 0
Remez inequality
In mathematics, the Remez inequality, discovered by the Soviet mathematician Evgeny Yakovlevich Remez, gives a bound on the sup norms of certain polynomials, the bound being attained by the Chebyshev
Fano's inequality
In information theory, Fano's inequality (also known as the Fano converse and the Fano lemma) relates the average information lost in a noisy channel to the probability of the categorization error. It
Weyl's inequality
In linear algebra, Weyl's inequality is a theorem about the changes to eigenvalues of an Hermitian matrix that is perturbed. It can be used to estimate the eigenvalues of a perturbed Hermitian matrix.
Khabibullin's conjecture on integral inequalities
In mathematics, Khabibullin's conjecture, named after , is related to Paley's problem for plurisubharmonic functions and to various extremal problems in the theory of entire functions of several varia
Eilenberg's inequality
Eilenberg's inequality, also known as the coarea inequality is a mathematical inequality for Lipschitz-continuous functions between metric spaces. Informally, it gives an upper bound on the average si
Van der Corput inequality
In mathematics, the van der Corput inequality is a corollary of the Cauchy–Schwarz inequality that is useful in the study of correlations among vectors, and hence random variables. It is also useful i
Golden–Thompson inequality
In physics and mathematics, the Golden–Thompson inequality is a trace inequality between exponentials of symmetric and Hermitian matrices proved independently by and . It has been developed in the con
Max–min inequality
In mathematics, the max–min inequality is as follows: For any function When equality holds one says that f, W, and Z satisfies a strong max–min property (or a saddle-point property). The example funct
Young's inequality for integral operators
In mathematical analysis, the Young's inequality for integral operators, is a bound on the operator norm of an integral operator in terms of norms of the kernel itself.