Copyright © 2009 M. Adil Khan et al. 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.
An improvement of the Jensen inequality for convex and monotone
function is given as well as various applications for mean. Similar results for
related inequalities of the Jensen type are also obtained. Also some applications
of the Cauchy mean and the Jensen inequality are discussed.