A sharp bound for the Chebyshev functional

TL;DR

This paper derives a precise upper bound for the Chebyshev functional involving absolutely continuous functions with bounded derivatives, enhancing understanding of their integral relationships.

Contribution

It provides a sharp bound for the Chebyshev functional specifically for functions with derivatives in L-infinity and L-one spaces, which was not previously established.

Findings

Established a sharp bound for the Chebyshev functional.

Applicable to functions with derivatives in L-infinity and L-one spaces.

Improves theoretical understanding of integral inequalities.

Abstract

In this work a sharp bound of the \v{C}eby\v{s}ev functional for absolutely continuous functions $f,g$ whose derivatives $f'\in L_{\infty}[a,b]$ and $g'\in L_{1}[a,b]$ is obtained.