A NEW PROOF OF POLYA-KNOPP'S INEQUALITY WITH AN EXTENSION

We show that a continuous version of Holder's inequality can give a new and direct proof of the Polya-Knopp type inequalities. We also have a single variable generalization of Polya-Knopp's inequality.

Automated summary

The continuous version of Holder's inequality provides a new and direct proof for Polya-Knopp type inequalities, and we also obtain a single variable generalization of Polya-Knopp's inequality.