Several refinements and counterparts of Radon's inequality

Abstract

We establish that the inequality of Radon is a particular case of Jensen's inequality. Starting from several refinements and counterparts of Jensen's inequality by Dragomir and Ionescu, we obtain a counterpart of Radon's inequality. In this way, using a result of Simić we find another counterpart of Radon's inequality. We obtain several applications using Mortici's inequality to improve Hölder's inequality and Liapunov's inequality. To determine the best bounds for some inequalities, we used Matlab program for different cases.

A Variant of Radon’s Inequality for Seminorms

“…Last decades mathematicians have paid attention to the Bergstron's and Radon's inequalities due to its originality, symmetry and quality among mathematical inequalities. New generalizations, refinements, modifications and significant developments of Bergstrom's and Radon's inequalities have been presented in [5][6][7][8][9][10][11][12][13], see also the references therein for the interested reader.…”