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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.

26D15Inequalities for sums, series and integrals of real functions
41A55Approximate quadratures
65D32Quadrature and cubature formulas (numerical methods)
Full Text: DOI
[1] Mitrinović, D. S.; Pečarić, J. E.; Fink, A. M.: Inequalities for functions and their integrals and derivatives. (1994)
[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, No. 11, 105-109 (1998) · Zbl 1072.26500