A note on the proofs of generalized radon inequality

TL;DR

This paper introduces generalized Radon inequalities, providing unified and simplified proofs, and explores their mathematical equivalences with other fundamental inequalities, along with various applications.

Contribution

It presents new generalized Radon inequalities with simplified proofs and establishes their equivalences with key classical inequalities.

Findings

Unified proofs for generalized Radon inequalities

Mathematical equivalences among major inequalities

Applications demonstrating the utility of the generalized inequalities

Abstract

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.