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...equality chain''', state the relationship between the [[harmonic mean]], [[geometric mean]], [[arithmetic mean]], and [[Root mean square|quadratic mean]] (also These inequalities often appear in mathematical competitions and have applications in many fie ...

In mathematics, the '''Besicovitch inequality''' is a [[Geometry|geometric inequality]] relating volume of a set and distances between certain subsets The Besicovitch inequality was used to prove [[systolic geometry|systolic inequalities]] ...

...positive numbers is greater than or equal to the sum of their two separate geometric means: By the [[inequality of arithmetic and geometric means]], we have: ...

...this mean to study other bivariate means and inequalities.<ref>E. Neuman, Inequalities for weighted sums of powers and their applications, ''Math. Inequal. Appl.' ...''J. Math. Inequal.'' 7 (2013), No. 3, 399–412</ref><ref>E. Neuman, Sharp inequalities involving Neuman–Sándor and logarithmic means, ''J. Math. Inequal.'' 7 (201 ...

...;→&nbsp;'''R''' is [[convex function|convex]], then the following chain of inequalities hold: ...rger, The Hermite-Hadamard Inequality in Higher Dimensions, The Journal of Geometric Analysis, 2019. ...

...ndom variable]],<ref>{{cite book|author=Pascal Massart|title=Concentration Inequalities and Model Selection: Ecole d'Eté de Probabilités de Saint-Flour XXXIII - 20 ...t2=Lugosi |first2=Gábor |last3=Massart |first3=Pascal |title=Concentration Inequalities: A Nonasymptotic Theory of Independence |date=2013 |publisher=Oxford Univer ...

...on of the vertices of a [[convex polytope]] specified by a [[set of linear inequalities]]:<ref>[[Eric W. Weisstein]] ''CRC Concise Encyclopedia of Mathematics,'' 2 ...e inverse ([[Duality (mathematics)|dual]]) problem of finding the bounding inequalities given the vertices is called ''[[facet enumeration]]'' (see [[convex hull a ...

...bounds on the variance with applications|journal= Journal of Mathematical Inequalities|volume=4|issue=3|pages= 355–363 |doi=10.7153/jmi-04-32 |doi-access=free}}</ Now, applying the [[Inequality of arithmetic and geometric means]], <math>ab \leq \left( \frac{a+b}{2} \right)^2</math>, with <math>a ...

An '''''n''-dimensional polyhedron''' is a geometric object that generalizes the 3-dimensional [[polyhedron]] to an ''n''-dimens ...perspective for problems in [[linear programming]].<ref name=":02">{{Cite Geometric Algorithms and Combinatorial Optimization}}</ref>{{Rp|page=9}} ...

Taking the real and imaginary parts of the logarithm, this implies the two inequalities ...given based on [[Goluzin's inequalities]], an equivalent form of Grunsky's inequalities (1939) for the [[Grunsky matrix]]. ...

In mathematics, the '''Lebedev–Milin inequality''' is any of several inequalities for the coefficients of the exponential of a [[power series]], found by {{h | title = Geometric Function Theory ...

...ohn Wiley & Sons|year=1988|isbn=0-471-91516-5|pages=209}}</ref> From the geometric point of view, {{math|'''B'''^T'''AB'''}} can be considered as th [[Category:Inequalities]] ...

...ausdorff dimension of self-similar [[stochastic processes]], such as the [[geometric Brownian motion]]{{sfn|Peres|Sousi|2016}} or stable [[Lévy processes]]{{sfn == Inequalities and identities == ...

...' in R^''n'', returns one of the following:<ref name=":0">{{Cite Geometric Algorithms and Combinatorial Optimization}}</ref>{{Rp|48}} ...considered, which allows for small errors in the boundary of ''K'' and the inequalities. Given a small error tolerance ''d''>0, we say that: ...

...Applications in Statistics and Matrix Theory |title=Analytic and Geometric Inequalities and Applications |pages=151–181 |doi=10.1007/978-94-011-4577-0_10 |isbn=978 ...quad \text{for } j = 1,\dots,n. </math><ref>{{cite book |title=Advances in Inequalities from Probability Theory and Statistics |first1=Neil S. |last1=Barnett |firs ...

...| last=Zhang | first=Gaoyong| title=Restricted chord projection and affine inequalities| journal=Geometriae Dedicata ...= 213–222| doi=10.1007/BF00182294| s2cid=123311639}}</ref> one of the few inequalities in convex geometry where simplices were proved to be extremals. He obtained ...

...4=M. |last5=Savage |first5=L. J. |last6=Sobel |first6=M. |date=1972 |title=Inequalities on the probability content of convex regions for elliptically contoured dis ...=2017 |chapter=Royen's Proof of the Gaussian Correlation Inequality |title=Geometric Aspects of Functional Analysis |series=Lecture Notes in Mathematics |volume ...

===Logarithmic Sobolev inequalities=== {{main|Logarithmic Sobolev inequalities}} ...

[[Category:Geometric inequalities]] ...

In [[graph theory]], the '''matching polytope''' of a given graph is a geometric object representing the possible [[Matching (graph theory)|matchings in the ...+x₃≤1, x₃+x₁≤1.''</blockquote>This set of inequalities represents a polytope in '''R'''³ - the 3-dimensional [[Euclidea ...