ON INEQUALITIES COMPLEMENTARY TO JENSEN’S INEQUALITY

Abstract

In this paper we give generalizations of two complementary inequalities proved by Pečarić and Mesihović. We also show that a generalization of Niculescu’s inequality obtained by M. Dincă, S. Rădulescu and M. Bencze is a simple consequence of an older theorem proved by Pečarić and Mesihović. We give an example which shows that a conjecture stated by M. Dincă, S. Rădulescu and M. Bencze is incorrect.