# List of inequalities

From Infogalactic: the planetary knowledge core

This page lists Wikipedia articles about named mathematical inequalities.

## 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's inequality
- Bohnenblust-Hille inequality
- Borell–Brascamp–Lieb inequality
- Brezis–Gallouet inequality
- Carleman's inequality
- Chebyshev–Markov–Stieltjes inequalities
- Chebyshev's sum inequality
- Clarkson's inequalities
- Eilenberg's inequality
- Duerinckx'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
- 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
- Trace inequalities
- Trudinger's theorem
- Turán's inequalities
- Von Neumann's inequality
- Wirtinger's inequality for functions

#### 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
- Young's inequality

### Combinatorics

- Binomial coefficient bounds
- Factorial bounds
- Fishburn–Shepp inequality
- Fisher's inequality
- Ingleton's inequality
- Lubell–Yamamoto–Meshalkin inequality
- Nesbitt's inequality
- Rearrangement inequality
- Schur's inequality
- Stirling's formula (bounds)

### Differential equations

### Geometry

See also: List of triangle inequalities

- Alexandrov–Fenchel inequality
- Aristarchus' inequality
- Barrow's inequality
- Berger–Kazdan comparison theorem
- 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
- 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

### Algebra

#### Linear algebra

- Abel's inequality
- Bregman–Minc inequality
- Cauchy–Schwarz inequality
- Golden–Thompson inequality
- Linear matrix inequality
- Peetre's inequality
- Triangle inequality
- von Neumann's trace inequality
- Weyl's inequality

### 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
- Burkholder's inequality
- Burkholder–Davis–Gundy inequalities
- Cantelli's inequality
- Chebyshev's inequality
- Chernoff's 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 isoperimetric inequality
- Gibbs' inequality
- Hoeffding's inequality
- Hoeffding's lemma
- Jensen's inequality
- Khintchine inequality
- Kolmogorov's inequality
- Kunita–Watanabe inequality
- Le Cam's theorem
- Marcinkiewicz–Zygmund inequality
- Markov's inequality
- McDiarmid's inequality
- Paley–Zygmund inequality
- Pinsker's inequality
- Popoviciu's inequality on variances
- Rao–Blackwell theorem
- Ross's conjecture, a lower bound on the average waiting time in certain queues
- Samuelson's inequality
- Shearer's inequality
- Simpson's paradox
- Talagrand's concentration inequality
- Vitale's random Brunn–Minkowski inequality
- Vysochanskiï–Petunin inequality

### Topology

## Inequalities particular to physics

- Ahlswede–Daykin inequality
- Bell's inequality – see Bell's theorem
- 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
- Sakurai's Bell inequality
- Tsirelson's inequality
- Wigner–d'Espagnat inequality