index of inequalities

Inequalities for reals and complex numbers

1. The triangle inequality. If $a,b,c$ are real numbers, then

   $$\left||a-c|-|b-c|\right|\le |a-b|\le |a-c|+|b-c|.$$

2. Nesbitt’s inequality

3. Young’s inequality (http://planetmath.org/YoungInequality)

4. Bernoulli’s inequality

5. Schur’s inequality

6. quadratic inequality

Inequalities in an inner product space

1. Cauchy-Schwarz-Bunyakovsky inequality (http://planetmath.org/CauchySchwarzInequality)

2. Bessel inequality

3. Peetre’s inequality

Inequalities for sequences

1. Shapiro inequality

2. MacLaurin’s inequality

3. Carleman’s inequality

4. arithmetic-geometric-harmonic means inequality and the general means inequality

5. Minkowski inequality

6. Chebyshev’s inequality and the rearrangement inequality

7. Muirhead’s theorem

Inequalities for functions

1. Jordan’s inequality for $\sin$

2. Jensen’s inequality

3. Gronwall’s inequality

4. Hölder inequality

5. Young’s inequality

6. Wirtinger’s inequality

Geometric inequalities

1. Hadwiger-Finsler inequality

2. Weizenbock’s inequality

3. Brunn-Minkowski inequality

Inequalities in number theory

1. inequality for fractions (http://planetmath.org/SummedNumeratorAndSummedDenominator)

2. Liouville approximation theorem

Matrix inequalities

1. Schur’s inequality (http://planetmath.org/ShursInequality)

2. Hadamard’s inequality

3. Wielandt-Hoffman theorem

4. Weyl’s inequality

5. Frobenius inequality

Inequalities for cardinal numbers

1. Cantor’s theorem

2. König’s theorem

Inequalities for random variables

1. Markov’s inequality

2. Kolmogorov’s inequality

3. Chebyshev’s inequality (http://planetmath.org/ChebyshevsInequality2)

Inequalities in order theory

1. distributive inequalities

Title	index of inequalities
Canonical name	IndexOfInequalities
Date of creation	2013-03-22 15:41:13
Last modified on	2013-03-22 15:41:13
Owner	matte (1858)
Last modified by	matte (1858)
Numerical id	15
Author	matte (1858)
Entry type	Topic
Classification	msc 54C30
Classification	msc 26-00
Classification	msc 12D99
Related topic	QuadraticInequality