Aczél's Inequality states that if or , then
Consider the function .
We have , and from we get . Therefore, must have at least one root, .
Let such that and let
be sequences of positive real numbers such that for . Then
with equality if and only if all the sequences are proportional.
Olympiad Suppose and are real numbers such that Prove that and . (USA TST 2004)
- Mascioni, Vania, A note on Aczél-type inequalities, JIPAM volume 3 (2002), issue 5, article 69.
- Popoviciu, T., Sur quelques inégalités, Gaz. Mat. Fiz. Ser. A, 11 (64) (1959) 451–461
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