Turkish Journal of Analysis and Number Theory
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Turkish Journal of Analysis and Number Theory. 2022, 10(1), 1-3
DOI: 10.12691/tjant-10-1-1
Open AccessArticle

Some Integral Inequalities for the Quadratic Functions of Bounded Variations and Application

M. A. Mustafa1, A. Qayyum1, , T. Hussain1 and M. Saleem1

1Institute of Southern Punjab, Multan-Pakistan

Pub. Date: January 09, 2022

Cite this paper:
M. A. Mustafa, A. Qayyum, T. Hussain and M. Saleem. Some Integral Inequalities for the Quadratic Functions of Bounded Variations and Application. Turkish Journal of Analysis and Number Theory. 2022; 10(1):1-3. doi: 10.12691/tjant-10-1-1

Abstract

In this paper, some essential inequalities are established for the quadratic function of bounded variation by using 7-step kernel. Some previous results are recaptured. Applications for quadrature rule and probability density function are also provided.

Keywords:
Ostrowski's inequality functions of bounded variations numerical integration

Creative CommonsThis 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]  A. Ostrowski, Uber die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert, Comment. Math. Helv. 10, No. 1, pp. 226-227, 1938.
 
[2]  A. Qayyum, M. Shoaib and S. Erden, On generaliźed fractional Ostrowski type inequalities for higher order derivatives, Communication in Mathematical Modeling And Applications, Vol. 4 (2), 2019.
 
[3]  A. Qayyum, M. Shoaib and I. Faye. On New Weighted Ostrowski Type inequalities Involving Integral Means over End Intervals and Application, Turkish Journal of Analysis and Number Theory, 3(2): 61-67, 2015.
 
[4]  A. R. Kashif, T. S. Khan, A. Qayyum and I. Faye, A comparison and error analysis of error bounds, International Journal of Analysis and Applications, 16 (5), 2018.
 
[5]  M. Iftikhar, A. Qayyum, S. Fahad and M. Arslan, A new version of Ostrowski type integral inequalities for different differentiable mapping, Open J. Math. Sci. Vol. 5(1), pp. 353-359, 2021.
 
[6]  S. Obiedat, M. A. Latif and A. Qayyum, Ostrowski type inequality using a 5-step weighted kernel, Internatioal Journal of Analysis and Applications, 13(3), 2019.
 
[7]  S. Obiedat, M. A. Latif and A. Qayyum, A weighted companion of Ostrowski’s inequalty using three step weighted kernel, Miskolc Mathematical Notes, Vol. 20, 2019.
 
[8]  S. S. Dragomir, The Ostrowski integral inequality for mappings of bounded variation, Bulletin of the Australian Mathematical Society, 60(1), pp. 495-508, 1999.
 
[9]  S. S. Dragomir, On the midpoint quadrature formula for mappings with bounded variation and applications, Kragujevac J. Math. 22, pp. 13-19, 2000.
 
[10]  S. S. Dragomir, On the Ostrowski’s integral inequality for mappings with bounded variation and applications, Mathematical Inequalities & Applications, 4, No.1, pp. 59-66, 2001.
 
[11]  S. S. Dragomir, Refinements of the generalised trapeźoid and Ostrowski inequalities for functions of bounded variation, Arch. Math. (Basel) 91, No. 5, pp. 450-460, 2008.
 
[12]  S. S. Dragomir, A companion of Ostrowski’s inequality for functions of bounded variation and applications, International Journal of Nonlinear Analysis and Applications, 5, No. 1, pp. 89-97, 2014.
 
[13]  P. Cerone, S. S. Dragomir and C. E. M. Pearce, A generaliźed trapeźoid inequality for functions of bounded variation, Turkish J. Math. 24, No. 2, pp. 147-163, 2000.
 
[14]  W. Liu and Y. Sun, A refinement of the companion of Ostrowski inequality for functions of bounded variation and Applications, arXiv:1207.3861v1, 2012.
 
[15]  H. Budak, M. Z. Sarikaya and A. Qayyum, Improvement in companion of Ostrowski type inequalities for mappings whose first derivatives are of bounded variation and applications, Filomat, 31: 13, 2017.
 
[16]  H. Budak and M. Z. Sarikaya and A. Qayyum, New refinements and applications of Ostrowski type inequalities for mappings whose nth derivatives are of bounded variation, TWMS J. App. Eng. Math. V.11, N.2, pp. 424-435, 2021.
 
[17]  H. Budak and M. Z. Sarikaya, A new Ostrowski type inequality for functions whose first derivatives are of bounded variation, Moroccan Journal of Pure and Applied Analysis, Vol. 2(1), pp. 1-11, 2016.
 
[18]  H. Budak and M. Z. Sarikaya, A companion of Ostrowski type inequalities for mappings of bounded variation and some applications, Transactions of A. Raźmadźe Mathematical Institute, 171(2), pp. 136-143, 2017.
 
[19]  H. Budak and M. Z. Sarikaya, New generaliźed inequalities for functions of bounded variation, Cumhuriyet Sci. J., Vol. 39-3, pp. 668-678, 2018.