EDB — 194

Exercises

1. [194] Prove Young inequality: given \(a,b{\gt}0\) and \(p,q{\gt}1\) such that \(1/p + 1/q = 1\) then

   \begin{equation} ab≤ \frac{a^ p} p+\frac{b^ q} q\label{eq:dis_ Young} \end{equation}

   42

   with equality if and only if \(a^ p = b^ q\); prove this using concavity of the logarithm.

   See also [1V7]↺↻.

   Solution 1

   [195]↺↻