List of inequalities

This article lists Wikipedia articles about named mathematical inequalities.

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
 * Chebyshev–Markov–Stieltjes inequalities
 * Chebyshev's sum inequality
 * Clarkson's inequalities
 * Eilenberg's inequality
 * Fekete–Szegő inequality
 * Fenchel's inequality
 * Friedrichs's 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

 * 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