Some companions of Ostrowski type inequality for functions whose second derivatives are convex and concave with applications. (English) Zbl 1308.26024

Summary: In this paper, we obtain some companions of Ostrowski type inequality for absolutely continuous functions whose second derivatives absolute values are convex and concave. Finally, we give some applications for special means.


26D10 Inequalities involving derivatives and differential and integral operators
26D15 Inequalities for sums, series and integrals
Full Text: DOI arXiv


[1] Liu, Zheng, Some companions of an Ostrowski type inequality and applications, JIPAM, 10, issue 2 (2009), art. 52 · Zbl 1168.26310
[2] Barnett, N. S.; Dragomir, S. S.; Gomma, I., A companion for the Ostrowski and the generalized trapezoid inequalities, J. Math. Comput. Modelling, 50, 179-187 (2009) · Zbl 1185.26038
[3] Ostrowski, A., Über die Absolutabweichung einer di erentierbaren Funktionen von ihren Integralmittelwort, Comment. Math. Helv., 10, 226-227 (1938)
[5] Alomari, M. W., A companion of Ostrowski’s inequality for mappings whose first derivatives are bounded and applications in numerical integration, Kragujevac J. Math., 36, 1, 77-82 (2012) · Zbl 1289.26037
[6] Dragomir, S. S., Some companions of Ostrowski’s inequality for absolutely continuous functions and applications, Bull. Korean Math. Soc., 42, 2, 213-230 (2005) · Zbl 1099.26015
[7] Kavurmaci, H.; Özdemir, M. E.; Avci, M., New Ostrowski type inequalities for \(m\)-convex functions and applications, Hacettepe J. Math. Statist., 40, 2, 135-145 (2011) · Zbl 1234.26030
[8] Liu, Z., Some Ostrowski type inequalities, Math. Comput. Modelling, 48, 949-960 (2008) · Zbl 1156.26305
[9] Latif, M. A.; Dragomir, S. S.; Matouk, A. E., New inequalities of Ostrowski type for co-ordinated \(s\)-convex functions via fractional integrals, J. Fract. Calculus Appl., 4, 1, 22-36 (2013) · Zbl 1488.26114
[10] Hussain, S., Generalization of Ostrowski and Čebyšev type inequalities involving many functions, Aequat. Math., 85, 3, 409-419 (2013) · Zbl 1277.26027
[11] Yue, H., Ostrowski inequality for fractional integrals and related fractional inequalities, TJMM, 5, 1, 85-89 (2013) · Zbl 1292.26067
[12] Set, E., New inequalities of Ostrowski type for mappings whose derivatives are \(s\)-convex in the second sense via fractional integrals, Comput. Math. Appl., 63, 1147-1154 (2012) · Zbl 1247.26038
[13] Set, E.; Sarikaya, M. Z., On the generalization of Ostrowski and Grüss type discrete inequalities, Comput. Math. Appl., 62, 455-461 (2011) · Zbl 1228.26029
[14] Alomari, M. W.; Özdemir, M. E.; Kavurmaci, H., On companion of Ostrowski inequality for mappings whose first derivatives absolute value are convex with applications, Miskolc Math. Notes, 13, 2, 233-248 (2012) · Zbl 1274.26032
[15] Kikianty, E.; Dragomir, S. S.; Cerone, P., Sharp inequalities of Ostrowski type for convex functions defined on linear spaces and application, Comput. Math. Appl., 56, 2235-2246 (2008) · Zbl 1165.26330
[17] Kavurmaci, H.; Avci, M.; Özdemir, M. E., New inequalities of Hermite-Hadamard type for convex functions with applications, J. Inequal. Appl, 2011, 86 (2011) · Zbl 1273.26031
[18] Özdemir, M.; Kavurmaci, H.; Akdemir, A.; Avci, M., Inequalities for convex and \(s\)-convex functions on \(\Delta = [a, b] \times [c, d]\), J. Inequal. Appl., 2012, 20 (2012) · Zbl 1279.26034
[19] Kirmaci, U. S., Improvement and further generalization of inequalities for differentiable mappings and applications, Comput. Math. Appl., 55, 485-493 (2008) · Zbl 1155.26308
[20] Pearce, C. E.M.; Pečarić, J., Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett., 13, 51-55 (2000) · Zbl 0970.26016
[21] Tseng, K.-L.; Hwang, S.-R.; Dragomir, S. S., New Hermite-Hadamard-type inequalities for convex functions (I), Appl. Math. Lett., 25, 1005-1009 (2012) · Zbl 1243.26013
[22] Tseng, K.-L.; Hwang, S.-R.; Dragomir, S. S., New Hermite-Hadamard-type inequalities for convex functions (II), Comput. Math. Appl., 62, 401-408 (2011) · Zbl 1228.26033
[23] Mitrinović, D. S.; Pečarić, J. E.; Fink, A. M., Classical and New Inequalities in Analysis (1993), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht/Boston/London, 740pp. · Zbl 0771.26009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.