Journal of Function Spaces

Journal of Function Spaces / 2009 / Article

Open Access

Volume 7 |Article ID 695685 | https://doi.org/10.1155/2009/695685

Aleksandra Čižmešija, Sabir Hussain, Josip Pečarić, "Some new refinements of strengthened Hardy and Pólya–Knopp's inequalities", Journal of Function Spaces, vol. 7, Article ID 695685, 20 pages, 2009. https://doi.org/10.1155/2009/695685

Some new refinements of strengthened Hardy and Pólya–Knopp's inequalities

Academic Editor: Lars-Erik Persson
Received01 Apr 2008

Abstract

We prove a new general one-dimensional inequality for convex functions and Hardy–Littlewood averages. Furthermore, we apply this result to unify and refine the so-called Boas's inequality and the strengthened inequalities of the Hardy–Knopp–type, deriving their new refinements as special cases of the obtained general relation. In particular, we get new refinements of strengthened versions of the well-known Hardy and Pólya–Knopp's inequalities.

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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