Augusta Raţiu, Babeş-Bolyai University, Faculty of Mathematics and Computer Science, No. 1 Mihail Kogalniceanu Street, RO-400084 Cluj-Napoca, Romania, e-mail: augu2003@yahoo.com; Nicuşor Minculete, Transilvania University, Faculty of Mathematics and Computer Science, No. 50 Street Iuliu Maniu, RO-500091 Braşov, Romania, e-mail: minculeten@yahoo.com
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 Simic 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.
Keywords: Radon's inequality; Jensen's inequality; Hölder's inequality; Liapunov's inequality
Classification (MSC 2010): 26D15
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