# An extension of Jensen's operator inequality and its application to Young inequality

## TL;DR

This paper extends Jensen's operator inequality to convexifiable functions, leading to new refinements and reverses of Young's inequality, with potential applications in operator theory.

## Contribution

It introduces a generalized Jensen's operator inequality for convexifiable functions, broadening the scope of classical inequalities.

## Key findings

- Derived a generalized Jensen's operator inequality for convexifiable functions.
- Provided new refinements and reverses of Young's inequality.
- Unified classical and new inequalities under a common framework.

## Abstract

Jensen's operator inequality for convexifiable functions is obtained. This result contains classical Jensen's operator inequality as a particular case. As a consequence, a new refinement and a reverse of Young's inequality is given.