engleski

Iyengar type estimate of error in trapezoidal rule

Using Hayashi's inequality, weighted Iyengar type inequality for functions with bounded higher derivatives is derived. This result generalizes results obtained in [P.Cerone, Generalised trapezoidal rules with error involving bounds of the n-th derivative, Math.Inequal.Appl. 5(3) (2002), 451-462] and [H.Gauchman, Some integral inequalities involving Taylor's remainder.I, Journal of Inequalities in Pure and Applied Mathematics, 3(2), Article 26, (2002)]. It also improves estimation obtained in [F.Qi, Inequalities for a weighted integral, Advanced Studies in Contemporary Mathematics (Kyungshang), 4(2) (2002), 93-101].

Iyengar's inequality; Steffensen's inequality; trapezoidal rule; bounded higher derivatives

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