# Some refinements of classical inequalities

## TL;DR

This paper introduces new refinements and reverses of classical Young inequalities for positive numbers and operators, compares them with existing results, and explores applications including those related to the Heron mean.

## Contribution

It presents novel refinements and reverses of Young inequalities for operators and numbers, along with applications and insights into the Heron mean.

## Key findings

- New refinements of Young inequalities introduced
- Reverses of classical inequalities established
- Applications to the Heron mean discussed

## Abstract

We give some new refinements and reverses Young inequalities in both additive-type and multiplicative-type for two positive numbers/operators. We show our advantages by comparing with known results. A few applications are also given. Some results relevant to the Heron mean are also considered.