Bulletin of the Australian Mathematical Society

Table of Contents - August 2010 - Volume 82, Issue 01  

Research Article

SUPERADDITIVITY OF SOME FUNCTIONALS ASSOCIATED WITH JENSEN’S INEQUALITY FOR CONVEX FUNCTIONS ON LINEAR SPACES WITH APPLICATIONS

S. S. DRAGOMIRa1

a1 Research Group in Mathematical Inequalities and Applications, School of Engineering and Science, Victoria University, PO Box 14428, Melbourne, Victoria 8001, Australia (email: sever.dragomir@vu.edu.au)

Abstract

Some new results related to Jensen’s celebrated inequality for convex functions defined on convex sets in linear spaces are given. Applications for norm inequalities in normed linear spaces and f-divergences in information theory are provided as well.

(Received September 17 2009)

2000 Mathematics subject classification

  • primary 26D15; secondary 94A17

Keywords and phrases

  • convex functions;
  • Jensen’s inequality;
  • norms;
  • mean f-deviation;
  • f-divergences