# Opial's inequality in $q$-Calculus revisited

## TL;DR

This paper revisits Opial's inequality within q-calculus, providing corrected proofs using elementary inequalities and the Gauchman q-restricted integral, offering a more straightforward approach.

## Contribution

It offers a fundamentally corrected and simplified proof of Opial's inequality in q-calculus, improving upon previous methods.

## Key findings

- Corrected proofs of Opial's inequality in q-calculus
- Introduction of a simple proof method based on elementary inequalities
- Application of Gauchman q-restricted integral

## Abstract

We have fundamentally corrected the proofs of the theorems from our paper [9] by giving an entirely different approach, using quite a simple method based on applications of some elementary inequalities, well-known H\"older's inequality, and the Gauchman $q$-restricted integral.