New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion

Hüseyin Budak; Fuat Usta; Mehmet Zeki Sarikaya

Research Article

New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion

Year 2018, Volume: 47 Issue: 3, 567 - 578, 01.06.2018

Hüseyin Budak Fuat Usta Mehmet Zeki Sarikaya

Abstract

In this paper, we have been introduced and tested some significant new bounds of Ostrowski type integral inequalities. In accordance with this purpose we have taken advantageous of the Taylor expansion for functions. Some numerical experiments have been given to show the applicability and accuracy of the proposed method.

Keywords

Ostrowski inequality, Taylor expansion

References

G. A. Anastassiou and S. S. Dragomir, On some estimates of the remainder in Taylor's formula, J. Math. Anal. Appl. 263 (2001), no. 1, 246263.
P. Cerone, S. S. Dragomir, J. Roumeliotis, An inequality of Ostrowski type for mappings whose second derivatives are bounded and applications, RGMIA Res. Rep. Coll., 1 (1998).
X.-L. Cheng. Improvement of some Ostrowski-Grüss type inequalities, Computers & Mathematics with Applications, 42, 109114, 2001.
S. S. Dragomir, S. Wang, An inequality of Ostrowski-Grüss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput. Math. Appl., 33 (1997), 1520.
S. S. Dragomir and S. Wang, An inequality of Ostrowski-Gruss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput. Math. Appl. 33 (1997), no. 11, 1520.
V. N. Huy and Q. A. Ngo, New bounds for the Ostrowski-like type inequalities, Bull. Korean Math. Soc. 48 (2011) 95-104.
A. R. Kashif, , M. Shoaib, M. A. Latif, Improved version of perturbed Ostrowski type inequalities for n-times dierentiable mappings with three-step kernel and its application, J. Nonlinear Sci. Appl. 9 (2016), 33193332.
M. E. Kiris and M. Z. Sarikaya, On Ostrowski type inequalities and Ceby²ev type inequalities, Filomat, 29:8 (2015), 16951713.
Z. Liu, Some OstrowskiGrüss type inequalities and applications, Comput. Math. Appl. 53 (2007) 7379.
Z. Liu, Some Ostrowski type inequalities, Math. Comput. Modelling 48 (2008) 949960.
W. Liu, New bounds for the companion of Ostrowski's inequality and applications, Filomat, 28 (2014), 167178.
A. M. Ostrowski, Über die absolutabweichung einer dierentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10(1938), 226-227.
M. Z. Sarikaya and H. Yaldiz, New generalization fractional inequalities of Ostrowski-Grüss type, Lobachevskii Journal of Math., 2013, Vol. 34, No. 4, pp. 326-331.
A. Qayyum, S. Hussain, A new generalized Ostrowski Gruss type inequality and applications, Appl. Math. Lett., 25 (2012),1875-1880.
N. Ujevi¢, New bounds for the rst inequality of Ostrowski-Grüss type and applications, Comput. Math. Appl., 46 (2003), 421427.

Year 2018, Volume: 47 Issue: 3, 567 - 578, 01.06.2018

Hüseyin Budak Fuat Usta Mehmet Zeki Sarikaya

Abstract

References

G. A. Anastassiou and S. S. Dragomir, On some estimates of the remainder in Taylor's formula, J. Math. Anal. Appl. 263 (2001), no. 1, 246263.
P. Cerone, S. S. Dragomir, J. Roumeliotis, An inequality of Ostrowski type for mappings whose second derivatives are bounded and applications, RGMIA Res. Rep. Coll., 1 (1998).
X.-L. Cheng. Improvement of some Ostrowski-Grüss type inequalities, Computers & Mathematics with Applications, 42, 109114, 2001.
S. S. Dragomir, S. Wang, An inequality of Ostrowski-Grüss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput. Math. Appl., 33 (1997), 1520.
S. S. Dragomir and S. Wang, An inequality of Ostrowski-Gruss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput. Math. Appl. 33 (1997), no. 11, 1520.
V. N. Huy and Q. A. Ngo, New bounds for the Ostrowski-like type inequalities, Bull. Korean Math. Soc. 48 (2011) 95-104.
A. R. Kashif, , M. Shoaib, M. A. Latif, Improved version of perturbed Ostrowski type inequalities for n-times dierentiable mappings with three-step kernel and its application, J. Nonlinear Sci. Appl. 9 (2016), 33193332.
M. E. Kiris and M. Z. Sarikaya, On Ostrowski type inequalities and Ceby²ev type inequalities, Filomat, 29:8 (2015), 16951713.
Z. Liu, Some OstrowskiGrüss type inequalities and applications, Comput. Math. Appl. 53 (2007) 7379.
Z. Liu, Some Ostrowski type inequalities, Math. Comput. Modelling 48 (2008) 949960.
W. Liu, New bounds for the companion of Ostrowski's inequality and applications, Filomat, 28 (2014), 167178.
A. M. Ostrowski, Über die absolutabweichung einer dierentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10(1938), 226-227.
M. Z. Sarikaya and H. Yaldiz, New generalization fractional inequalities of Ostrowski-Grüss type, Lobachevskii Journal of Math., 2013, Vol. 34, No. 4, pp. 326-331.
A. Qayyum, S. Hussain, A new generalized Ostrowski Gruss type inequality and applications, Appl. Math. Lett., 25 (2012),1875-1880.
N. Ujevi¢, New bounds for the rst inequality of Ostrowski-Grüss type and applications, Comput. Math. Appl., 46 (2003), 421427.

There are 15 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Mathematics
Authors	Hüseyin Budak Fuat Usta Mehmet Zeki Sarikaya
Publication Date	June 1, 2018
Published in Issue	Year 2018 Volume: 47 Issue: 3

Cite

APA	Budak, H., Usta, F., & Sarikaya, M. Z. (2018). New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion. Hacettepe Journal of Mathematics and Statistics, 47(3), 567-578.
AMA	Budak H, Usta F, Sarikaya MZ. New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion. Hacettepe Journal of Mathematics and Statistics. June 2018;47(3):567-578.
Chicago	Budak, Hüseyin, Fuat Usta, and Mehmet Zeki Sarikaya. “New Upper Bounds of Ostrowski Type Integral Inequalities Utilizing Taylor Expansion”. Hacettepe Journal of Mathematics and Statistics 47, no. 3 (June 2018): 567-78.
EndNote	Budak H, Usta F, Sarikaya MZ (June 1, 2018) New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion. Hacettepe Journal of Mathematics and Statistics 47 3 567–578.
IEEE	H. Budak, F. Usta, and M. Z. Sarikaya, “New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 3, pp. 567–578, 2018.
ISNAD	Budak, Hüseyin et al. “New Upper Bounds of Ostrowski Type Integral Inequalities Utilizing Taylor Expansion”. Hacettepe Journal of Mathematics and Statistics 47/3 (June 2018), 567-578.
JAMA	Budak H, Usta F, Sarikaya MZ. New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion. Hacettepe Journal of Mathematics and Statistics. 2018;47:567–578.
MLA	Budak, Hüseyin et al. “New Upper Bounds of Ostrowski Type Integral Inequalities Utilizing Taylor Expansion”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 3, 2018, pp. 567-78.
Vancouver	Budak H, Usta F, Sarikaya MZ. New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion. Hacettepe Journal of Mathematics and Statistics. 2018;47(3):567-78.