kb/data/en.wikipedia.org/wiki/List_of_inequalities-0.md

title	chunk	source	category	tags	date_saved	instance
List of inequalities	1/1	https://en.wikipedia.org/wiki/List_of_inequalities	reference	science, encyclopedia	2026-05-05T08:15:09.363624+00:00	kb-cron

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 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 ===

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