List of inequalities

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This article lists Wikipedia articles about named mathematical inequalities.

## Contents

* 1 Inequalities in pure mathematics
* 1.1 Analysis
* 1.1.1 Inequalities relating to means
* 1.2 Combinatorics
* 1.3 Differential equations
* 1.4 Geometry
* 1.5 Information theory
* 1.6 Algebra
* 1.6.1 Linear algebra
* 1.6.1.1 Eigenvalue inequalities
* 1.7 Number theory
* 1.8 Probability theory and statistics
* 1.9 Topology
* 2 Inequalities particular to physics
* 3 See also

## Inequalities in pure mathematics

### Analysis

* Agmon's inequality
* Askey–Gasper inequality
* Babenko–Beckner inequality
* Bernoulli's inequality
* Bernstein's inequality (mathematical analysis)
* Bessel's inequality
* Bihari–LaSalle inequality
* Bohnenblust–Hille inequality
* Borell–Brascamp–Lieb inequality
* Brezis–Gallouet inequality
* Carleman's inequality
* Carlson's inequality
* Chebyshev–Markov–Stieltjes inequalities
* Chebyshev's sum inequality
* Clarkson's inequalities
* Eilenberg's inequality
* Fekete–Szegő inequality
* Fenchel's inequality
* Friedrichs' inequality
* Gagliardo–Nirenberg interpolation inequality
* Gårding's inequality
* Grothendieck inequality
* Grunsky's inequalities
* Hanner's inequalities
* Hardy's inequality
* Hardy–Littlewood inequality
* Hardy–Littlewood–Sobolev inequality
* Harnack's inequality
* Hausdorff–Young inequality
* Hermite–Hadamard inequality
* Hilbert's inequality
* Hölder's inequality
* Jackson's inequality
* Jensen's inequality
* Khabibullin's conjecture on integral inequalities
* Kantorovich inequality
* Karamata's inequality
* Korn's inequality
* Ladyzhenskaya's inequality
* Landau–Kolmogorov inequality
* Lebedev–Milin inequality
* Lieb–Thirring inequality
* Littlewood's 4/3 inequality
* Markov brothers' inequality
* Mashreghi–Ransford inequality
* Max–min inequality
* Minkowski's inequality
* Poincaré inequality
* Popoviciu's inequality
* Prékopa–Leindler inequality
* Rayleigh–Faber–Krahn inequality
* Remez inequality
* Riesz rearrangement inequality
* Schur test
* Shapiro inequality
* Sobolev inequality
* Steffensen's inequality
* Szegő inequality
* Three spheres inequality
* Trace inequalities
* Trudinger's theorem
* Turán's inequalities
* Von Neumann's inequality
* Wirtinger's inequality for functions
* Young's convolution inequality
* Young's inequality for products

#### Inequalities relating to means

* Hardy–Littlewood maximal inequality
* Inequality of arithmetic and geometric means
* Ky Fan inequality
* Levinson's inequality
* Maclaurin's inequality
* Mahler's inequality
* Muirhead's inequality
* Newton's inequalities
* Stein–Strömberg theorem

### Combinatorics

* Binomial coefficient bounds
* Factorial bounds
* XYZ inequality
* Fisher's inequality
* Ingleton's inequality
* Lubell–Yamamoto–Meshalkin inequality
* Nesbitt's inequality
* Rearrangement inequality
* Schur's inequality
* Shapiro inequality
* Stirling's formula (bounds)

### Differential equations

* Grönwall's inequality

### Geometry

See also: List of triangle inequalities

* Alexandrov–Fenchel inequality
* Aristarchus's inequality
* Barrow's inequality
* Berger–Kazdan comparison theorem
* Blaschke–Lebesgue inequality
* Blaschke–Santaló inequality
* Bishop–Gromov inequality
* Bogomolov–Miyaoka–Yau inequality
* Bonnesen's inequality
* Brascamp–Lieb inequality
* Brunn–Minkowski inequality
* Castelnuovo–Severi inequality
* Cheng's eigenvalue comparison theorem
* Clifford's theorem on special divisors
* Cohn-Vossen's inequality
* Erdős–Mordell inequality
* Euler's theorem in geometry
* Gromov's inequality for complex projective space
* Gromov's systolic inequality for essential manifolds
* Hadamard's inequality
* Hadwiger–Finsler inequality
* Hinge theorem
* Hitchin–Thorpe inequality
* Isoperimetric inequality
* Jordan's inequality
* Jung's theorem
* Loewner's torus inequality
* Łojasiewicz inequality
* Loomis–Whitney inequality
* Melchior's inequality
* Milman's reverse Brunn–Minkowski inequality
* Milnor–Wood inequality
* Minkowski's first inequality for convex bodies
* Myers's theorem
* Noether inequality
* Ono's inequality
* Pedoe's inequality
* Ptolemy's inequality
* Pu's inequality
* Riemannian Penrose inequality
* Toponogov's theorem
* Triangle inequality
* Weitzenböck's inequality
* Wirtinger inequality (2-forms)

### Information theory

* Inequalities in information theory
* Kraft's inequality
* Log sum inequality
* Welch bounds

### Algebra

* Abhyankar's inequality
* Pisier–Ringrose inequality

#### Linear algebra

* Abel's inequality
* Bregman–Minc inequality
* Cauchy–Schwarz inequality
* Golden–Thompson inequality
* Hadamard's inequality
* Hoffman-Wielandt inequality
* Peetre's inequality
* Sylvester's rank inequality
* Triangle inequality
* Trace inequalities

##### Eigenvalue inequalities

* Bendixson's inequality
* Weyl's inequality in matrix theory
* Cauchy interlacing theorem
* Poincaré separation theorem

### Number theory

* Bonse's inequality
* Large sieve inequality
* Pólya–Vinogradov inequality
* Turán–Kubilius inequality
* Weyl's inequality

### Probability theory and statistics

* Azuma's inequality
* Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount
* Bhatia–Davis inequality, an upper bound on the variance of any bounded probability distribution
* Bernstein inequalities (probability theory)
* Boole's inequality
* Borell–TIS inequality
* BRS-inequality
* Burkholder's inequality
* Burkholder–Davis–Gundy inequalities
* Cantelli's inequality
* Chebyshev's inequality
* Chernoff's inequality
* Chung–Erdős inequality
* Concentration inequality
* Cramér–Rao inequality
* Doob's martingale inequality
* Dvoretzky–Kiefer–Wolfowitz inequality
* Eaton's inequality, a bound on the largest absolute value of a linear combination of bounded random variables
* Emery's inequality
* Entropy power inequality
* Etemadi's inequality
* Fannes–Audenaert inequality
* Fano's inequality
* Fefferman's inequality
* Fréchet inequalities
* Gauss's inequality
* Gauss–Markov theorem, the statement that the least-squares estimators in certain linear models are the best linear unbiased estimators
* Gaussian correlation inequality
* Gaussian isoperimetric inequality
* Gibbs's inequality
* Hoeffding's inequality
* Hoeffding's lemma
* Jensen's inequality
* Khintchine inequality
* Kolmogorov's inequality
* Kunita–Watanabe inequality
* Le Cam's theorem
* Lenglart's inequality
* Marcinkiewicz–Zygmund inequality
* Markov's inequality
* McDiarmid's inequality
* Paley–Zygmund inequality
* Pinsker's inequality
* Popoviciu's inequality on variances
* Prophet inequality
* Rao–Blackwell theorem
* Ross's conjecture, a lower bound on the average waiting time in certain queues
* Samuelson's inequality
* Shearer's inequality
* Stochastic Gronwall inequality
* Talagrand's concentration inequality
* Vitale's random Brunn–Minkowski inequality
* Vysochanskiï–Petunin inequality

### Topology

* Berger's inequality for Einstein manifolds

## Inequalities particular to physics

* Ahlswede–Daykin inequality
* Bell's inequality - see Bell's theorem
* Bell's original inequality
* CHSH inequality
* Clausius–Duhem inequality
* Correlation inequality – any of several inequalities
* FKG inequality
* Ginibre inequality
* Griffiths inequality
* Heisenberg's inequality
* Holley inequality
* Leggett–Garg inequality
* Riemannian Penrose inequality
* Rushbrooke inequality
* Tsirelson's inequality

## See also

* Comparison theorem
* List of mathematical identities
* Lists of mathematics topics
* List of set identities and relations

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