Copyright © 2012 J. Pečarić and M. Ribičić Penava. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 spaces. Generalizations of Simpson’s
3/8 formula and the Lobatto four-point formula with related inequalities are
considered as special cases.