New converses of Jensen inequality via Green functions with applications

Abstract

The Jensen inequality has many applications in several fields such as mathematics, statistics and economics etc. There are a lot of results devoted to the Jensen inequality concerning refinements, generalizations and converses etc. The main aim of this paper is to use new idea and present converses of the Jensen inequality with the help of Green functions. By virtue of these results, we obtain converses of Holder and Levinson’s inequalities. At the end we present several applications of these results in information theory. The idea used in this paper may stimulate further research for the Jensen inequality.