engleski

On corrected Bullen-Simpson's inequality

The aim of this paper is to derive corrected Bullen-Simpson's inequality, starting from corrected Simpson's and dual corrected Simpson's formula. By corrected we mean formulae that approximate the integral not only with the values of the function in certain points but also with the value of the first derivative in end points of the interval. These formulae will have a higher degree of exactness than formulae derived in [M.Matić, J.Pečarić, A.Vukelić, On generalization of Bullen-Simpson's inequality, Rocky Mountain J. Math. 35(2005), 1727-1754.].

three-point quadrature formulae; corrected Simpson's and corrected dual Simpson's formulae; convex functions; Bernoulli polynomials; functions of bounded variation; Lipschitz functions

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