On corrected Bullen-Simpson's 3/8 inequality (CROSBI ID 115161)
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Franjić, Iva ; Pečarić, Josip
engleski
On corrected Bullen-Simpson's 3/8 inequality
The aim of this paper is to derive corrected Bullen-Simpson's 3/8 inequality, starting from corrected Simpson's 3/8 and corrected Maclaurin'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.]
quadrature formulae; corrected Simpson's 3/8 and corrected Maclaurin's formulae; convex functions; Bernoulli polynomials; functions of bounded variation; Lipschitzian functions
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Matematika