Minkowski Inequality
Revision as of 12:57, 12 November 2010 by Spanferkel (talk | contribs) (→Equivalence with the standard form)
The Minkowski Inequality states that if is a nonzero real number, then for any positive numbers , the following holds:
Notice that if either or is zero, the inequality is equivalent to Holder's Inequality.
Equivalence with the standard form
For , putting and , the above becomes
.
Put and we get the form in which the Minkowski Inequality is given most often:
As the latter can be iterated, there is no loss of generality by putting .
Problems
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