Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
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.
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