Copyright © 2009 Peng Gao. 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.

Abstract

We extend the results in parts I–III on certain inequalities involving the weighted power means as well as the symmetric means. These inequalities can be largely viewed as concerning the bounds for ratios of differences of means and can be traced back to the work of Diananda.