  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.
