# index of inequalities

## Inequalities for reals and complex numbers

1. 1.

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

 $\bigl{|}|a-c|-|b-c|\bigr{|}\leq|a-b|\leq|a-c|+|b-c|.$
2. 2.

Nesbitt’s inequality

3. 3.

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

4. 4.

Bernoulli’s inequality

5. 5.

Schur’s inequality

6. 6.

## Inequalities in an inner product space

1. 1.

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

2. 2.

Bessel inequality

3. 3.

Peetre’s inequality

## Inequalities for sequences

1. 1.
2. 2.

MacLaurin’s inequality

3. 3.

Carleman’s inequality

4. 4.
5. 5.
6. 6.

Chebyshev’s inequality and the rearrangement inequality

7. 7.

## Inequalities for functions

1. 1.

Jordan’s inequality for $\sin$

2. 2.

Jensen’s inequality

3. 3.

Gronwall’s inequality

4. 4.

Hölder inequality

5. 5.

Young’s inequality

6. 6.

Wirtinger’s inequality

## Geometric inequalities

1. 1.
2. 2.

Weizenbock’s inequality

3. 3.

## Inequalities in number theory

1. 1.

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

2. 2.

## Matrix inequalities

1. 1.

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

2. 2.

3. 3.
4. 4.

Weyl’s inequality

5. 5.

## Inequalities for cardinal numbers

1. 1.

Cantor’s theorem

2. 2.

König’s theorem

## Inequalities for random variables

1. 1.

Markov’s inequality

2. 2.

Kolmogorov’s inequality

3. 3.

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

## Inequalities in order theory

1. 1.

distributive inequalities

Title index of inequalities IndexOfInequalities 2013-03-22 15:41:13 2013-03-22 15:41:13 matte (1858) matte (1858) 15 matte (1858) Topic msc 54C30 msc 26-00 msc 12D99 QuadraticInequality