# Bounds for the difference between two \v{C}eby\v{s}ev functionals

## TL;DR

This paper generalizes the pre-Grüss inequality and provides new bounds for the difference between two Chebyshev functionals, enhancing understanding of their relationships in mathematical analysis.

## Contribution

It introduces a generalized form of the pre-Grüss inequality and derives multiple bounds for the difference between two Chebyshev functionals.

## Key findings

- Established a generalized pre-Grüss inequality.
- Derived several bounds for Chebyshev functional differences.
- Enhanced theoretical understanding of Chebyshev inequalities.

## Abstract

In this work, a generalization of pre-Gr\"{u}ss inequality is established. Several bounds for the difference between two \v{C}eby\v{s}ev functional are proved.