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International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 283127, 7 pages
http://dx.doi.org/10.1155/2013/283127
Research Article

On Some Intermediate Mean Values

Mathematical Institute SANU, Kneza Mihaila 36, 11000 Belgrade, Serbia

Received 25 June 2012; Revised 9 December 2012; Accepted 16 December 2012

Academic Editor: Mowaffaq Hajja

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.