Iyengar type estimate of error in trapezoidal rule (CROSBI ID 122772)
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Franjić, Iva ; Pečarić, Josip ; Perić, Ivan
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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