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Sharp error bounds for some quadrature formulae and applications. (English) Zbl 1182.65048

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.

MSC:

65D32 Numerical quadrature and cubature formulas
26D10 Inequalities involving derivatives and differential and integral operators
41A55 Approximate quadratures

Citations:

Zbl 0996.26016
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