Ujević, Nenad Sharp error bounds for some quadrature formulae and applications. (English) Zbl 1182.65048 JIPAM, J. Inequal. Pure Appl. Math. 7, No. 1, Paper No. 8, 11 p. (2006). Summary: In the author’s article ”A generalization of the pre-Grüss inequality and applications to some quadrature formulae” [JIPAM, J. Inequal. Pure Appl. Math. 3, No. 1, Paper No. 13, 9 p., electronic only (2002; Zbl 0996.26016)] error bounds for some quadrature formulae are established. Here we prove that all inequalities (error bounds) obtained in this article are sharp. We also establish a new sharp averaged midpoint-trapezoid inequality and give applications in numerical integration. Cited in 1 Document MSC: 65D32 Numerical quadrature and cubature formulas 26D10 Inequalities involving derivatives and differential and integral operators 41A55 Approximate quadratures Keywords:sharp error bounds; quadrature formulae; numerical integration Citations:Zbl 0996.26016 PDFBibTeX XMLCite \textit{N. Ujević}, JIPAM, J. Inequal. Pure Appl. Math. 7, No. 1, Paper No. 8, 11 p. (2006; Zbl 1182.65048) Full Text: EuDML EMIS