On a General Inequality with Applications

Abstract

A general set-valued inequality is proved in two analogical forms. As applications we obtain some simple inequalities for convex, concave, subadditive and superadditive functions. We also point out that some classical inequalities (e.g., those by Minkowski and by Beckenbach and Dresher) and some fairly new results (e.g. by Pearic and Beesack [7] and Peetre and Persson [81) are special cases of our results.