This article lists Wikipedia articles about named mathematical inequalities.

Inequalities in pure mathematics

Analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

* 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 In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality (mathematics), inequality between Lebesgue integration, integrals and an indispensable tool for the study of Lp space, spaces. The numbers an ...

* 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 In mathematics, the Shapiro inequality is an inequality proposed by Harold S. Shapiro in 1954. Statement of the inequality Suppose is a natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly exc ...

* 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
mean A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statist ...
s

* Hardy–Littlewood maximal inequality *

Inequality of arithmetic and geometric means Inequality may refer to: * Inequality (mathematics), a relation between two quantities when they are different. * Economic inequality, difference in economic well-being between population groups ** Income inequality, an unequal distribution of in ...

* Ky Fan inequality * Levinson's inequality * Maclaurin's inequality * Mahler's inequality * Muirhead's inequality * Newton's inequalities * Stein–Strömberg theorem

Combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

* 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 *

* Stirling's formula (bounds)

Differential equations

* Grönwall's inequality

Geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

Triangle inequality In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side. This statement permits the inclusion of Degeneracy (mathematics)#T ...

* Weitzenböck's inequality * Wirtinger inequality (2-forms)

Information theory Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...

* Inequalities in information theory * Kraft's inequality * Log sum inequality * Welch bounds

Algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

* Abhyankar's inequality * Pisier–Ringrose inequality

Linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...

* Abel's inequality * Bregman–Minc inequality *

Cauchy–Schwarz inequality The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is an upper bound on the absolute value of the inner product between two vectors in an inner product space in terms of the product of the vector norms. It is ...

* Golden–Thompson inequality * Hadamard's inequality * Hoffman-Wielandt inequality * Peetre's inequality * Sylvester's rank inequality *

* Trace inequalities

= Eigenvalue inequalities

= * Bendixson's inequality * Weyl's inequality in matrix theory * Cauchy interlacing theorem * Poincaré separation theorem

Number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

* Bonse's inequality * Large sieve inequality * Pólya–Vinogradov inequality * Turán–Kubilius inequality * Weyl's inequality

Probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
and
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

* 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 In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in ...

, 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 In probability theory, Popoviciu's inequality, named after Tiberiu Popoviciu, is an upper bound on the variance ''σ''2 of any bounded probability distribution. Let ''M'' and ''m'' be upper and lower bounds on the values of any random variable ...

* 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 Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

* Berger's inequality for Einstein manifolds

Inequalities particular to physics

* Ahlswede–Daykin inequality * Bell's inequality – see

Bell's theorem Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measuremen ...

** 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