Several refinements and counterparts of Radon's inequality

摘要

summary: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.