List of inequalities explained

This article 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–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

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

• 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

• 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