A note on the proofs of generalized radon inequality

In this paper, we introduce and prove the generalizations of Radon inequality. The proofs in the paper unify and are simpler than those in former work. Meanwhile, we also find mathematical equivalences among the Bernoulli inequality, the weighted AM-GM inequality, the H\"{o}lder inequality, the weighted power mean inequality and the Minkowski inequality. Finally, a series of the applications are shown in this note.