On Generalization of Dragomir’s Inequalities

Hüseyin Budak^1, and Mehmet Zeki Sarıkaya¹

¹Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey

Cite this paper:
Hüseyin Budak and Mehmet Zeki Sarıkaya. On Generalization of Dragomir’s Inequalities. Turkish Journal of Analysis and Number Theory. 2017; 5(5):191-196. doi: 10.12691/tjant-5-5-5

Abstract

In this paper, we establish some generalization of weighted Ostrowski type integral inequalities for functions of bounded variation.

Keywords:
Function of bounded variation Ostrowski type inequalities Riemann-Stieltjes integrals

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Alomari, M. W., “A Generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation,” RGMIA Research Report Collection, 14, 2011, Article 87, 11 pp.
[2]	Alomari, M. W. and Latif, M.A. “Weighted companion for the Ostrowski and the generalized trapezoid inequalities for mappings of bounded variation,” RGMIA Research Report Collection, 14, 2011, Article 92, 10 pp.
[3]	Cerone, P. Cheung, W.S. and Dragomir, S.S., “On Ostrowski type inequalities for Stieltjes integrals with absolutely continuous integrands and integrators of bounded variation,” Computers and Mathematics with Applications, 54, 2007, 183-191.
[4]	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.
[5]	Dragomir, S. S., “The Ostrowski integral inequality for mappings of bounded variation,” Bull.Austral. Math. Soc., 60(1), 1999, 495-508.
[6]	Dragomir, S. S., “On the midpoint quadrature formula for mappings with bounded variation and applications,” Kragujevac J. Math. 22, 2000, 13-19.
[7]	Dragomir, S. S., “On the Ostrowski's integral inequality for mappings with bounded variation and applications,” Math. Inequal. Appl. 4(1), 2001, 59-66.
[8]	Dragomir, S. S., “A companion of Ostrowski's inequality for functions of bounded variation and applications,” Int. J. Nonlinear Anal. Appl. 5(1), 2014, 89-97.
[9]	Dragomir, S. S., “Refinements of the generalised trapezoid and Ostrowski inequalities for functions of bounded variation.” Arch. Math. (Basel) 91(5), 2008, 450-460.
[10]	Dragomir, S.S. and Momoniat, E., “A Three point quadrature rule for functions of bounded variation and applications,” RGMIA Research Report Collection, 14, 2011, Article 33, 16 pp.
[11]	Dragomir, S. S., “Some perturbed Ostrowski type inequalities for functions of bounded variation,” RGMIA Res. Rep. Coll. 16, 2013, Art. 93.
[12]	Liu, W. and Sun, Y., “A Refinement of the companion of Ostrowski inequality for functions of bounded variation and Applications,” arXiv:1207.3861v1, 2012.
[13]	Mishra, V.N., “Some problems on approximations of functions in banach spaces,” Ph.D. Thesis (2007), Indian Institute of Technology, Roorkee 247 667, Uttarakhand, India.
[14]	Mishra V.N. and Mishra, L.N., “Trigonometric approximation of signals (Functions) in LP (p≥1)-norm,” International Journal of Contemporary Mathematical Sciences, 7(19), 2012, 909-918.
[15]	Mishra, L.N., “On existence and behavior of solutions to some nonlinear integral equations with Applications,” Ph.D. Thesis (2017), National Institute of Technology, Silchar 788010, Assam, India.
[16]	Ostrowski, A., M. “Über die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert,” Comment. Math. Helv. 10, 1938, 226-227.
[17]	Tseng, K-L, Yang, G-S and Dragomir, S. S., “Generalizations of weighted trapezoidal inequality for mappings of bounded variation and their applications,” Mathematical and Computer Modelling, 40, 2004, 77-84.
[18]	Tseng, K-L, “Improvements of some inequalites of Ostrowski type and their applications,” Taiwan. J. Math. 12(9), 2008, 2427-2441.
[19]	Tseng, K-L, Hwang, S-R, Yang, G-S and Chou, Y-M, “Improvements of the Ostrowski integral inequality for mappings of bounded variation I,” Applied Mathematics and Computation 217, 2010, 2348-2355.
[20]	Tseng, K-L, Hwang, S-R, Yang, G-S and Chou, Y-M, “Weighted Ostrowski ,ntegral ,nequality for mappings of bounded variation,“ Taiwanese J. of Math., 15(2), 2011, 573-585.
[21]	Tseng, K-L, “Improvements of the Ostrowski integral inequality for mappings of bounded variation II,” Applied Mathematics and Computation 218, 2012, 5841-5847.