Maclaurin’s inequalities for functions whose first derivatives are preinvex

Abstract

In this paper, using a new identity, we study one of the famous Newton-Cotes three-point quadraturerules. More precisely Maclaurin’s quadrature rule, for which we establish the error estimate of this methodunder the constraint that the first derivatives belong to the class of preinvex functions. We also give someapplications to special means as applications. We believe that this new studied inequality and the resultsobtained in this article will further inspire intrigued researchers.