We consider families of general two-point quadrature formulae, using the extension of Montgomery's identity via Taylor's formula. The formulae obtained are used to present a number of inequalities for functions whose derivatives are from L p spaces and Bullentype inequalities.2000 Mathematics subject classification: primary 26D15; secondary 26D20, 41A55.

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We present new generalizations of the weighted Montgomery identity constructed by using the Hermite interpolating polynomial. The obtained identities are used to establish new generalizations of weighted Ostrowski type inequalities for differentiable functions of class $C^{n}$ C n . Also, we consider new bounds for the remainder of the obtained identities by using the Chebyshev functional and certain Grüss type inequalities for this functional. By applying those results we derive inequalities for the class of n-convex functions.

Abstract. We derive some new bounds for the general three-point quadrature formulae of Euler type using some inequalities for the Chebyshev functional. As special cases, we provide some new error estimates for Euler Simpson formula, dual Euler Simpson formula and Euler Maclaurin formula. Also, applications for Euler Bullen-Simpson formula are obtained.Mathematics subject classification (2010): 26D15, 26D20, 26D99.