Copyright © 2013 Slavko Simic. 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 give a necessary and sufficient mean condition for the quotient of two Jensen functionals and define a new class of mean values where are continuously differentiable convex functions satisfying the relation ,  . Then we asked for a characterization of such that the inequalities or hold for each positive , where are the harmonic, arithmetic, logarithmic, and identric means, respectively. For a subclass of with , this problem is thoroughly solved.