# New Refinements for integral and sum forms of H\"older inequality

## TL;DR

This paper introduces new refinements for the integral and sum forms of H"older inequality, enhancing existing inequalities and demonstrating their improvements through applications.

## Contribution

The paper presents novel refinements of H"older inequality for both integral and sum forms, improving upon existing inequalities and showcasing their practical applications.

## Key findings

- New refined inequalities for H"older inequality
- Improved bounds for related inequalities
- Practical applications demonstrating the refinements

## Abstract

In this paper, new refinements for integral and sum forms of H\"older inequality are established. We note that many existing inequalities related to the H\"older inequality can be improved via obtained new inequalities in here, we show this in an application.