A note on the proofs of generalized Radon inequality

Abstract

In this paper, we introduce and prove several generalizations of the Radon inequality. The proofs in the current paper unify and also are simpler than those in early published work. Meanwhile, we find and show the mathematical equivalences among the Bernoulli inequality, the weighted AM-GM inequality, the Hölder inequality, the weighted power mean inequality and the Minkowski inequality. Finally, some applications involving the results proposed in this work are shown.

Keywords

• the Bergström inequality
• the Radon inequality
• the weighted power mean inequality
• equivalence
• the Hölder inequality