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
Fishburn–Shepp 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
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
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
Marcinkiewicz–Zygmund inequality
Markov's inequality
McDiarmid's inequality
Paley–Zygmund inequality
Pinsker's inequality
Popoviciu's inequality on variances
Rao–Blackwell theorem
Ross's conjecture, a lower bound on the average waiting time in certain queues
Samuelson's inequality
Shearer's 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
Sakurai's Bell inequality
Tsirelson's inequality
Wigner–d'Espagnat inequality
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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