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 andthe general means inequality

5. Minkowski inequality

6. Chebyshev’s inequalityand 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