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

الملخص EN

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.