No Access

On generalization of weighted Ostrowski type inequalities for functions of bounded variation

Huseyin Budak

Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey

E-mail Address: hsyn.budak@gmail.com

Corresponding author.

Search for more papers by this author

and

Mehmet Zeki Sarikaya

Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey

E-mail Address: sarikayamz@gmail.com

Search for more papers by this author

https://doi.org/10.1142/S1793557118500493Cited by:3 (Source: Crossref)

Abstract

In this paper, some generalization of weighted Ostrowski type integral inequalities for mappings of bounded variation are obtained and some interesting inequalities as special cases are given.

Communicated by W. S. Cheung

Keywords:

AMSC: 26D15, 26A45, 26D10

References

1. M. W. Alomari, A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation, RGMIA Res. Rep. Coll. 14 (2011), Article ID: 87, 11 pp. Google Scholar
2. M. W. Alomari and M. A. Latif, Weighted companion for the Ostrowski and the generalized trapezoid inequalities for mappings of bounded variation, RGMIA Res. Rep. Coll. 14 (2011), Article ID: 92, 10 pp. Google Scholar
3. H. Budak and M. Z. Sarikaya, On generalization of Dragomir’s inequalities, Eurasian Math. J., in press. Google Scholar
4. H. Budak and M. Z. Sarikaya, A new generalization of Ostrowski type inequality for mappings of bounded variation, RGMIA Res. Rep. Coll. 18 (2015), Article ID: 47, 9 pp. Google Scholar
5. P. Cerone, W. S. Cheung and S. S. Dragomir, On Ostrowski type inequalities for Stieltjes integrals with absolutely continuous integrands and integrators of bounded variation, Comput. Math. Appl. 54 (2007) 183–191. Crossref, Web of Science, Google Scholar
6. P. Cerone, S. S. Dragomir and C. E. M. Pearce, A generalized trapezoid inequality for functions of bounded variation, Turk. J. Math. 24 (2000) 147–163. Google Scholar
7. S. S. Dragomir, The Ostrowski integral inequality for mappings of bounded variation, Bull. Austral. Math. Soc. 60(1) (1999) 495–508. Crossref, Web of Science, Google Scholar
8. S. S. Dragomir, On the midpoint quadrature formula for mappings with bounded variation and applications, Kragujevac J. Math. 22 (2000) 13–19. Google Scholar
9. S. S. Dragomir, On the Ostrowski’s integral inequality for mappings with bounded variation and applications, Math. Inequal. Appl. 4(1) (2001) 59–66. Web of Science, Google Scholar
10. S. S. Dragomir, Refinements of the generalised trapezoid and Ostrowski inequalities for functions of bounded variation, Arch. Math. (Basel) 91(5) (2008) 450–460. Crossref, Web of Science, Google Scholar
11. S. S. Dragomir, Some perturbed Ostrowski type inequalities for functions of bounded variation, RGMIA Res. Rep. Coll. 16 (2013), Article ID: 93. Google Scholar
12. S. S. Dragomir, A companion of Ostrowski’s inequality for functions of bounded variation and applications, Int. J. Nonlinear Anal. Appl. 5(1) (2014) 89–97. Google Scholar
13. S. S. Dragomir and E. Momoniat, A three point quadrature rule for functions of bounded variation and applications, RGMIA Res. Rep. Coll. 14 (2011), Article ID: 33, 16 pp. Google Scholar
14. Z. Liu, Another generalization of weighted Ostrowski type inequality for mappings of bounded variation, Appl. Math. Lett. 25 (2012) 393–397. Crossref, Web of Science, Google Scholar
15. W. Liu and Y. Sun, A refinement of the companion of Ostrowski inequality for functions of bounded variation and applications, preprint (2012), arXiv:1207.3861v1. Google Scholar
16. A. M. Ostrowski, Über die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10 (1938) 226–227. Crossref, Google Scholar
17. K.-L. Tseng, Improvements of some inequalites of Ostrowski type and their applications, Taiwan. J. Math. 12(9) (2008) 2427–2441. Crossref, Web of Science, Google Scholar
18. K.-L. Tseng, Improvements of the Ostrowski integral inequality for mappings of bounded variation II, Appl. Math. Comput. 218 (2012) 5841–5847. Crossref, Web of Science, Google Scholar
19. K.-L. Tseng, S.-R. Hwang, G.-S. Yang and Y.-M. Chou, Improvements of the Ostrowski integral inequality for mappings of bounded variation I, Appl. Math. Comput. 217 (2010) 2348–2355. Crossref, Web of Science, Google Scholar
20. K.-L. Tseng, S.-R. Hwang, G.-S. Yang and Y.-M. Chou, Weighted Ostrowski integral inequality for mappings of bounded variation, Taiwanese J. Math. 15(2) (2011) 573–585. Crossref, Web of Science, Google Scholar
21. K.-L. Tseng, G.-S. Yang and S. S. Dragomir, Generalizations of weighted trapezoidal inequality for mappings of bounded variation and their applications, Math. Comput. Modell. 40 (2004) 77–84. Crossref, Web of Science, Google Scholar