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On generalizations of Ostrowski inequality and some related results. (English) Zbl 1013.26020
Summary: Some generalizations of the Ostrowski inequality, the Milovanović-Pečarić-Fink inequality, the Dragomir-Agarwal inequality and the Hadamard inequality are given.

MSC:
26D15 Inequalities for sums, series and integrals
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[1] A. Ostrowski: Über die Absolutabweichung einer differentierbaren Funktionen von ihren Integralmittelwort. Comment. Math. Helv. 10 (1938), 226-227. · Zbl 0018.25105 · doi:10.1007/BF01214290 · eudml:138699
[2] D. S. Mitrinović, J. Pečarić and A. M. Fink: Inequalities Involving Functions and Their Integrals and Derivatives. Kluwer Acad. Publ., Dordrecht, 1991. · Zbl 0744.26011
[3] G. V. Milovanović and J. E. Pečarić: On generalizations of the inequality of A. Ostrowski and some related applications. Univ. Beograd. Publ. Elektrotehn. Fak., Ser. Mat. Fiz., No 544-No 576 (1976), 155-158.
[4] A. M. Fink: Bounds of the derivation of a function from its avereges. Czechoslovak Math. J. 42(117) (1992), 289-310. · Zbl 0780.26011 · eudml:31283
[5] S. S. Dragomir and S. Wang: A new inequality of Ostrowski’s type in \(L_1\)-norm and applications to some special means and to some numerical quadrature rules. Thamkang J. Math. 28 (1997), 239-244. · Zbl 0888.26013
[6] S. S. Dragomir and S. Wang: A new inequality of Ostrowski’s type in \(L_p\)-norm and applications to some special means and to some numerical quadrature rules. Thamkang J. Math · Zbl 0888.26013
[7] M. Matić and J. Pečarić and N. Ujević: On new estimation of the remainder in generalized Taylor’s formula. Math. Inequal. Appl. 2 (1999), 343-361. · Zbl 0933.26013
[8] S. S. Dragomir and R. P. Agarwal: The inequalities for differential mappings and applications to special means of real numbers and to trapezoidal formula. Appl. Math. Lett. 11 (1998), 91-95. · Zbl 0938.26012 · doi:10.1016/S0893-9659(98)00086-X
[9] C. E. M. Pearce and J. Pečarić: Inequalities for differential mappings with applications to special means and quadrature formulas. Appl. Math. Lett 13 (2000), 51-55. · Zbl 0970.26016 · doi:10.1016/S0893-9659(99)00164-0
[10] Handbook of mathematical functions with formulae, graphs and mathematical tables. National Bureau of Standards, Applied Math. Series 55, 4th printing. M. Abramowitz, I. A. Stegun (eds.), Washington, 1965.
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