Sharp Integral Inequalities Based on a General Four-Point Quadrature Formula via a Generalization of the Montgomery Identity

Abstract

We consider families of general four-point quadrature formulae using a generalization of the Montgomery identity via Taylor’s formula. The results are applied to obtain some sharp inequalities for functions whose derivatives belong to 𝐿𝑝 spaces. Generalizations of Simpson’s 3/8 formula and the Lobatto four-point formula with related inequalities are considered as special cases.