engleski

General Euler-Ostrowski formulae and applications to quadratures

The aim of this paper is to generalize an inequality obtained in [A.Aglić-Aljinović, M.Matić, J.Pečarić, Improvements of some Ostrowski type inequalities, J.Comput.Anal.Appl., in press] and therefore obtain a generalization and improvement of an inequality obtained in [G.A.Anastassiou, Univariate Ostrowski inequalities, Revisited, Monatsh Math (135):175-189 (2002)]. To do this, first we derive the general Euler-Ostrowski formulae which generalize extended Euler formulae, obtained in [Lj.Dedić, M.Matić, J.Pečarić, On generalizations of Ostrowski inequality via some Euler-type identities, Math. Inequal. Appl. 3(3): 337-353 (2000)]. The main novelty is that a remainder is expressed in terms of B_n*(x-mt) which enables us to obtain a wide variety of quadrature formulae such as trapezoid, midpoint, bitrapezoid, twopoint formulae and their multipoint generalizations.

Ostrowski's inequality; extended Euler formulae; Bernoulli polynomials; quadrature formulae

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