ON THE OSTROWSKI-GRUSS TYPE ¨ INEQUALITY FOR TWICE DIFFERENTIABLE FUNCTIONS

Abstract

In this paper we obtain some new Ostrowski-Gr¨uss type inequalities containing twice differentiable functions

Keywords

• Ostrowski-Gr¨uss Inequality,2000 AMS Classification: Primary: 26 D 15

ON THE OSTROWSKI-GRUSS TYPE ¨ INEQUALITY FOR TWICE DIFFERENTIABLE FUNCTIONS

Abstract

References

1. Anastassiou, G. A. Ostrowski type inequalities, Proc. Amer. Math. Soc. 123, 3775–3781, 1995.
2. Cerone, P, Dragomir, S. S. Roumeliotis, J. An inequality of Ostrowski-Gr¨uss type for twice differentiable mappings and applications in numerical integration, KYUNGPOOK Math. J. 39(2), 331–341, 1999.
3. Cheng, X. L. Improvement of some Ostrowski-Gr¨uss type inequalities, Computers & Math- ematics with Applications 42 (1/2), 109–114, 2001.
4. Dragomir, S. S. and Wang, S. An inequality of Ostrowski-Gr¨uss 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), 15–20, 1997.
5. Feng, Q. and Meng, F. Some generalized Ostrowski–Gr¨uss type integral inequalities, Com- puters & Mathematics with Applications 63 (3), 652–659, 2012.
6. Liu, Z. Some Ostrowski Gr¨uss type inequalities and applications, Computers & Mathematics with Applications 53, 73–79, 2007.
7. Liu, Z. A sharp generalized Ostrowski-Gr¨uss inequality, Tamsui Oxford Journal of Mathe- matical Sciences 24 (2), 175–184, 2008.
8. Mati´c, M., Peˇcari´c, J. and Ujevi´c, N. Improvement and further generalization of some inequalities of Ostrowski-Gr¨uss type, Computers & Mathematics with Applications 39 (3/4), 161–175, 2000.

9. Milovanovi´c, G. V. and Peˇcari´c, J. E. On generalization of the inequality of A. Ostrowski and some related applications, Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz. (544-576), 155–158, 1976.
10. Niezgoda, M. A new inequality of Ostrowski–Gr¨uss type and applications to some numerical quadrature rules, Computers & Mathematics with Applications 58 (3), 589–596, 2009.
11. Ostrowski, A. ¨Uber die Absolutabweichung einer differentierbaren Funktion von ihren Inte- gralmittelwert, Comment. Math. Helv. 10, 226–227, 1938.
12. ¨Ozdemir, M. E., Kavurmacı, H. and Set, E. Ostrowski’s type inequalities for (α, m)-convex functions
13. Pachpatte, B. G. On ˇCebyˇsev-Gr¨uss type inequalities via Peˇcari´c’s extension of the Mont- gomery identity, J. Inequal. Pure Appl. Math. 7 (1), Article 11, 2006.
14. Pearce, C. E. M., Peˇcari´c, J., Ujevi´c, N. and Varoˇs, S. Generalizations of some inequalities of Ostrowski Gr¨uss type, Math. Inequal. Appl. 3 (1), 25–34, 2000.
15. Sarıkaya, M. Z. On the Ostrowski type integral inequality, Acta Math. Univ. Comenianee LXXIX(1), 129–134, 2010.
16. Tong, F. and Guan, L. A simple proof of the generalized Ostrowski-Gr¨uss type integral inequality, Int. Journal of Math. Analysis 2 (18), 889–892, 2008.
17. Ujevi´c, N. New bounds for the first inequality of Ostrowski-Gr¨uss type and applications, Computers & Mathematics with Applications 46, 421–427, 2003.
18. Yang, S. A unified approach to some inequalities of Ostrowski–Gr¨uss type, Computers & Mathematics with Applications 51, 1047–1056, 2006.