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# index of inequalities

# Inequalities for reals and complex numbers

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. Nesbitt’s inequality

3. 4. Bernoulli’s inequality

5. Schur’s inequality

6.

# Inequalities in an inner product space

1. 2. 3. Peetre’s inequality

# Inequalities for sequences

1. 2. MacLaurin’s inequality

3. Carleman’s inequality

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

5. 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

# Matrix inequalities

1. 2. Hadamard’s inequality

3. Wielandt-Hoffman theorem

4. Weyl’s inequality

5.

# 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.

# Inequalities in order theory

Related:

QuadraticInequality

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## Mathematics Subject Classification

54C30*no label found*26-00

*no label found*12D99

*no label found*

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