Journal of Inequalities and Applications 
Volume 5 (2000), Issue 6, Pages 639-666
doi:10.1155/S1025583400000357

Generalizations of weighted version of Ostrowski’s inequality and some related results

M. Matić,1 J. Pečarić,2 and N. Ujević3

 1FESB, Department of Mathematics, University of Sprit, R. Boškovića bb, Sprit 21000, Croatia
2Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, Zagreb 10000, Croatia
3Department of Mathematics, University of Split, Teslina 12, Sprit 21000, Croatia
Received 13 July 1999; Revised 11 September 1999

Abstract

We establish some new weighted integral identities and use them to prove a number of inequalities of Ostrowski type. Among other results, we generalize one result related to the weighted version of the Ostrowski’s inequality of Pečarić and Savić (Zbornik radova VA KoV (Beograd), 9 (1983), 171–202) as well as the recent result of Roumeliotis et al. (RGMIA, 1(1) (1998)). We also show that the recent Anastassiou’s generalization (Proc. Amer. Math. Soc., 123 (1995), 3775–3781) of the Ostrowski’s inequality is a special case of some results from this paper.