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Category: Inequality

Easy Induction Proof of Arithmetic Geometric Mean Inequality

July 3rd, 2009, No Comments

The Arithmetic-Geometric mean inequality says that If then and equality happens if and only if all ‘s are equal. The case for is trivial and for is equivalent to which is equivalent to . So the statement is true for . Now assume that the statement is true for . Without lost of generality we [...]

A Nice Implication of Holder’s Inequality

June 29th, 2009, No Comments

First let us recall the statement of Holder’s inequality: Holder’s Inequality Let are non-negative real numbers. Let be two numbers that satisfy . Then and the inequality becomes an equality iff for some constant . The proof of this can be read from the previous post here. Now let us consider a particular case of [...]

Holder’s Inequality

June 24th, 2009, 2 Comments

The Holder’s Inequality is a direct generalization of the Cauchy-Schwarz’s inequality. The statement is the following Holder’s Inequality Let are non-negative real numbers. Let be two numbers that satisfy . Then and the inequality becomes an equality iff for some constant . One can easily see that the Cauchy-Schwarz inequality is exactly the Holder’s inequality [...]

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