List of inequalities

This page lists Wikipedia articles about named mathematical inequalities.

Inequalities in pure mathematics

=Analysis=

* Askey–Gasper inequality
* Bernoulli's inequality
* Bernstein's inequality (mathematical analysis)
* Bessel's inequality
* Borell-Brascamp-Lieb inequality
* Carleman's inequality
* Chebyshev-Markov-Stieltjes inequalities
* Chebyshev's sum inequality
* Clarkson's inequalities
* Fenchel's inequality
* Friedrichs' inequality
* Gårding's inequality
* Grothendieck inequality
* Hanner's inequalities
* Hardy's inequality
* Harnack's inequality
* Hermite–Hadamard inequality
* Hölder's inequality
* Jackson's inequality
* Jensen's inequality
* Kantorovich inequality
* Korn's inequality
* Landau-Kolmogorov inequality
* Lebedev–Milin inequality
* Markov brothers' inequality
* Minkowski's inequality
* Poincaré inequality
* Remez inequality
* Shapiro inequality
* Sobolev inequality
* Steffensen's inequality
* Trudinger's theorem
* Turán's inequalities
* Von Neumann's inequality
* Wirtinger's inequality for functions

Inequalities relating to means

* Inequality of arithmetic and geometric means
* Ky Fan inequality
* MacLaurin's inequality
* Muirhead's inequality
* Newton's inequalities
* Young's inequality

Combinatorics

* Fisher's inequality
* Lubell-Yamamoto-Meshalkin inequality
* Nesbitt's inequality
* Rearrangement inequality
* Schur's inequality

Differential equations

* Grönwall's inequality

Geometry

* Barrow's inequality
* Bishop-Gromov inequality
* Brascamp-Lieb inequality
* Brunn-Minkowski 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
* Isoperimetric inequality
* Jung's theorem
* Loewner's torus inequality
* Loomis-Whitney inequality
* Milman's reverse Brunn-Minkowski inequality
* Minkowski's first inequality for convex bodies
* Ono's inequality
* Pedoe's inequality
* Ptolemy's inequality
* Pu's inequality
* Riemannian Penrose inequality
* Triangle inequality
* Weitzenböck's inequality
* Wirtinger inequality (2-forms)

Information theory

* Inequalities in information theory
* Kraft's inequality

Linear algebra

* Abel's inequality
* Cauchy-Schwarz inequality
* Golden-Thompson inequality
* Peetre's inequality
* Triangle inequality
* Weyl's inequality

Number theory

* Large sieve inequality
* Pólya-Vinogradov inequality
* Weyl's inequality

Probability theory

* An inequality on location and scale parameters (of probability distributions)
* Azuma's inequality
* Bernstein inequalities (probability theory)
* Boole's inequality
* Chebyshev's inequality
* Chernoff's inequality
* Cramér-Rao inequality
* Dvoretzky-Kiefer-Wolfowitz inequality
* Entropy power inequality
* Etemadi's inequality
* Gaussian isoperimetric inequality
* Gibbs' inequality
* Hoeffding's inequality
* Kolmogorov's inequality
* le Cam's theorem
* Markov's inequality
* McDiarmid's inequality
* Paley–Zygmund inequality
* Vitale's random Brunn-Minkowski inequality
* Vysochanskiï-Petunin inequality

Topology

* Berger's inequality for Einstein manifolds

Inequalities particular to physics

* Bell's inequality — see Bell's theorem
** Bell's original inequality
* Heisenberg's inequality
* Riemannian Penrose inequality
* Rushbrooke inequality
* Tsirelson's inequality