On two inequalities of Čebyšev

Abstract

In this work, several sharp bounds for the Čebyšev functional involving various type of functions are proved. In particular, for the Čebyšev functional of two absolutely continuous functions whose first derivatives are both convex, convex and belong to Lp-spaces, convex and of bounded variation, convex and satisfies Lipschitz condition; new sharp bounds are presented. Other related results regarding two convex and concave functions are given.