On multidimensional Ostrowski type inequalities

Abstract

Sharp Ostrowski type inequalities for multidimensional sets and functions of bounded variations are proved.

References

Ostrowski, Alexander. Über die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert. (German) Comment. Math. Helv. 10 (1937), no. 1, 226–227. https://doi.org/10.1007/bf01214290

Anastassiou, George A. Advanced inequalities. Series on Concrete and Applicable Mathematics, 11. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2011. xii+410 pp. ISBN: 978-981-4317-62-7; 981-4317-62-4

Ostrowski type inequalities and applications in numerical integration. Edited by Sever S. Dragomir and Themistocles M. Rassias. Kluwer Academic Publishers, Dordrecht, 2002. xx+481 pp. ISBN: 1-4020-0562-8. https://doi.org/10.1007/978-94-017-2519-4

Dragomir, Silvestru Sever. Operator inequalities of Ostrowski and trapezoidal type. SpringerBriefs in Mathematics. Springer, New York, 2012. x+112 pp. ISBN: 978-1-4614-1778-1 https://doi.org/10.1007/978-1-4614-1779-8_3

Kovalenko, Oleg V. Ostrowski type inequalities for sets and functions of bounded variation. J. Inequal. Appl. 2017, Paper No. 151, 16 pp. https://doi.org/10.1186/s13660-017-1429-5

Kronrod, A. S. О функциях двух переменных. (Russian) [O funkcijah dvuh peremennyh] Успехи мат. наук [Uspehi mat. nauk], 5 (1950), no. 1, 24–134.

Vitushkin, A. G. О многомерных вариациях. (Russian) [O mnogomernyh variacijah] Gostehteorizdat, Moskva (1955).

Ivanov, L. D. Вариации множеств и функций. (Russian) [Variations of sets and functions] Edited by A. G. Vituškin. Izdat. ``Nauka'', Moscow, 1975. 352 pp.

Published
29.04.2020
How to Cite
KovalenkoО. V. “On Multidimensional Ostrowski Type Inequalities”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 5, Apr. 2020, pp. 644–657, doi:10.37863/umzh.v72i5.1125.
Section
Research articles