Several applications of Cartwright-Field's inequality

TL;DR

This paper explores various applications of Cartwright-Field's inequality, demonstrating its utility in deriving and connecting fundamental inequalities in mathematics, including Young's, Bernoulli's, and Hölder's inequalities.

Contribution

The paper introduces multiple new applications of Cartwright-Field's inequality across different mathematical contexts, expanding its relevance and utility.

Findings

Derived Young's, Bernoulli's, and Hölder's inequalities using Cartwright-Field's inequality

Established connections between weighted power means and other inequalities

Presented applications to arithmetic functions and operator inequalities

Abstract

In this paper we present several applications of Cartwright-Field's inequality. Among these we found Young's inequality, Bernoulli's inequality, the inequality between the weighted power means, H\"{o}lder's inequality and Cauchy's inequality. We give also two applications related to arithmetic functions and to operator inequalities.