On the Ostrowski-Grüss type inequality for twice differentiable functions
On the Ostrowski-Grüss type inequality for twice differentiable functions
In this paper we obtain some new Ostrowski-Gr ̈uss type inequalities containing twice differentiable functions.
___
- [1] Anastassiou, G. A. Ostrowski type inequalities, Proc. Amer. Math. Soc. 123, 37753781, 1995.
- [2] Cerone, P, Dragomir, S. S. Roumeliotis, J. An inequality of Ostrowski-Gruss type for twice differentiable mappings and applications in numerical inte gration, KYUNGPOOK Math. J. 39 (2), 331341, 1999.
- [3] Cheng, X.L. Improvement of some Ostrowski-Gr ̈uss type inequalities, Computers & Math- ematics with Applications 42 (1/2), 109114, 2001.
- [4] Dragomir, S.S. and Wang, S. An inequality of Ostrowski-Gruss type and its applications to the estimation of error bounds for some special means and for some numeraical quadrature rules, Computers & Mathematics with Applications 33 (11), 1520, 1997.
- [5] Feng, Q. and Meng, F. Some generalized OstrowskiGruss type integral inequalities, Com-puters & Mathematics with Applications 63(3), 652659, 2012.
- [6] Liu, Z. Some Ostrowski Gruss type inequalities and applications, Computers & Mathematics with Applications 53, 7379, 2007.
- [7] Liu, Z.A sharp generalized Ostrowski-Gruss inequality, Tamsui Oxford Journal of Mathe-matical Sciences 24 (2), 175184, 2008.
- [8] Matic, M., Pecaric, J. and Ujevic, N.Improvement and further generalization of some inequalities of Ostrowski-Gruss type, Computers & Mathematics with Applications 39(3/4),161175, 2000.
- [9] Milovanovic, G.V. and Pecaric, J. E.On generalization of the inequality of A. Ostrowski and some related applications, Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz. (544-576),155158, 1976.
- [10] Niezgoda, M.A new inequality of OstrowskiGruss type and applications to some numerical quadrature rules, Computers & Mathematics with Applications 58 (3), 589596, 2009.
- [11] Ostrowski, A. Uber die Absolutabweichung einer differentierbaren Funkti on von ihren Inte-gralmittelwert, Comment. Math. Helv. 10, 226227, 1938.
- [12]Ozdemir, M.E., Kavurmacı, H. and Set, E. Ostrowskis type inequalities for (α, m)-convex functions, KYUNGPOOK Math. J. 50, 371378, 2010.
- [13] Pachpatte, B.G. On Cebysev-Gruss type inequalities via Pecarics extens ion of the Mont-gomery identity, J. Inequal. Pure Appl. Math. 7 (1), Article 11, 2006.
- [14] Pearce, C.E.M., Pecaric, J., Ujevic, N. and Varos, S. Generalizations of some inequalities of Ostrowski Gr ̈uss type, Math. Inequal. Appl.3 (1), 2534, 2000.
- [15] Sarıkaya, M.Z.On the Ostrowski type integral inequality, Acta Math. Univ. Comenianee LXXIX (1), 129134, 2010.
- [16] Tong, F. and Guan, L.A simple proof of the generalized Ostrowski-Gr ̈uss type int egralinequality, Int. Journal of Math. Analysis 2(18), 889892, 2008.
- [17] Ujevic, N.New bounds for the first inequality of Ostrowski-Gruss type and applications, Computers & Mathematics with Applications 46, 421427, 2003.
- [18] Yang, S. A unified approach to some inequalities of OstrowskiGruss type, Computers & Mathematics with Applications 51, 10471056, 2006.