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A new generalization of Ostrowski’s integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means. (English) Zbl 0946.26013

Summary: We establish a new inequality of Ostrowski type for functions with bounded derivatives. This has immediate applications in numerical integration where new estimates are obtained for the remainder term of the trapezoid, midpoint, and Simpson formulae. Applications to special means are also investigated.

MSC:

26D15 Inequalities for sums, series and integrals
26E60 Means
41A55 Approximate quadratures
65D32 Numerical quadrature and cubature formulas
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References:

[1] Mitrinović, D.S.; Pečarić, J.E.; Fink, A.M., Inequalities for functions and their integrals and derivatives, (1994), Kluwer Academic Dordrecht · Zbl 0744.26011
[2] Dragomir, S.S.; Wang, S., Applications of Ostrowski’s inequality to the estimation of error bounds for some special means and for some numerical quadrature rules, Appl. math. lett., 30, 11, 105-109, (1998) · Zbl 1072.26500
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