Young's inequality


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Young's inequality

[′yəŋz ‚in·ə′kwäl·əd·ē]
(mathematics)
An inequality that applies to a function y = f (x) that is continuous and strictly increasing for x ≥ 0 and satisfies f (0) = 0, with inverse function x = g (y); it states that, for any positive numbers a and b in the ranges of x and y, respectively, the product ab is equal to or less than the sum of the integral from 0 to a of f (x) dx and the integral from 0 to b of g (y) dy.
References in periodicals archive ?
The proof is based on the multiplier method and makes use of some properties of convex functions including the use of the general Young's inequality and Jensen's inequality.
Then, Young's inequality, with [sigma] = 2p - 1 and [sigma]' = [2p - 1/2p - 2], gives
Tominaga, showed the reverse inequality for Young's inequality, using Specth's ratio, thus
2), we make use of Young's inequality, which says for any two nonnegative real numbers w and z, we have
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