Weighted Ostrowski's Type Integral Inequalities for Mapping Whose Second Derivative is Bounded

Muhammad Arslan; Muhammad Amir Mustafa; Shah Fahad; Irfan Waheed; Ather Qayyum

doi:10.32323/ujma.1151207

EN

Weighted Ostrowski's Type Integral Inequalities for Mapping Whose Second Derivative is Bounded

Abstract

The aim of this paper is to concentrate on the domain of $L_{\infty },$ $% L_{p},$ and $L_{1}$ norms of inequalities and their applications for some special weight functions. For different weights some previous results are recaptured. Applications are also discussed.

Keywords

Ostrowski Inequality, Weight Function, Numerical Integration.

Supporting Institution

n/a

Project Number

n/a

Thanks

n/a

References

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[3] S. S. Dragomir, S. Wang, A new inequality of Ostrowski’ s type in L1 ( ˆ J;ˇk), and applications to some special means and some numerical quadrature rules, Tamkang J. Math., 28 (1997), 239-244.
[4] M. Z. Sarıkaya, E. Set, On New Ostrowski type integral inequalities, Thai J. Math., 12(1) (2014), 145-154.
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[8] A. Qayyum, I. Faye, M. Shoaib, M. A. Latif, A generalization of Ostrowski type inequality for mappings whose second derivatives belong to L1 (Jˆ; ˇk) and applications, Int. J. Pure Appl. Math. Sci., 98(2) (2015), 169-180.
[9] A. Qayyum, A. R. Kashif, M. Shoaib, I. Faye, Derivation and applications of inequalities of Ostrowski type for n-times differentiable mappings for cumulative distribution function and some quadrature rules, J. Nonlinear Sci. Appl., 9(4) (2016), 1844–1857.
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[13] S. Fahad, M. A. Mustafa, Z. Ullah, T. Hussain, A. Qayyum, Weighted Ostrowski’s type integral inequalities for mapping whose first derivative is bounded, Int. J. Anal. Appl., 20(16) (2022), 13 pages.
[14] M. Iftikhar, A. Qayyum, S, Fahad, M. Arslan, A new version of Ostrowski type integral inequalities for different differentiable mapping, Open J. Math. Sci., 5(1) (2021), 353-359.
[15] M. A. Mustafa, A. Qayyum, T. Hussain, M. Saleem, Some integral inequalities for the quadratic functions of bounded variations and application, Turkish Journal of Analysis and Number Theory, 10(1) (2022), 1-3.
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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Muhammad Arslan
Pakistan

Muhammad Amir Mustafa
Pakistan

Shah Fahad
Türkiye

Irfan Waheed
Türkiye

Ather Qayyum ^*
Pakistan

Publication Date

December 29, 2022

Submission Date

July 30, 2022

Acceptance Date

October 18, 2022

Published in Issue

Year 2022 Volume: 5 Number: 4

DOI

https://doi.org/10.32323/ujma.1151207

IZ

https://izlik.org/JA93XZ28EJ

APA

Arslan, M., Mustafa, M. A., Fahad, S., Waheed, I., & Qayyum, A. (2022). Weighted Ostrowski’s Type Integral Inequalities for Mapping Whose Second Derivative is Bounded. Universal Journal of Mathematics and Applications, 5(4), 122-129. https://doi.org/10.32323/ujma.1151207

AMA

1.Arslan M, Mustafa MA, Fahad S, Waheed I, Qayyum A. Weighted Ostrowski’s Type Integral Inequalities for Mapping Whose Second Derivative is Bounded. Univ. J. Math. Appl. 2022;5(4):122-129. doi:10.32323/ujma.1151207

Chicago

Arslan, Muhammad, Muhammad Amir Mustafa, Shah Fahad, Irfan Waheed, and Ather Qayyum. 2022. “Weighted Ostrowski’s Type Integral Inequalities for Mapping Whose Second Derivative Is Bounded”. Universal Journal of Mathematics and Applications 5 (4): 122-29. https://doi.org/10.32323/ujma.1151207.

EndNote

Arslan M, Mustafa MA, Fahad S, Waheed I, Qayyum A (December 1, 2022) Weighted Ostrowski’s Type Integral Inequalities for Mapping Whose Second Derivative is Bounded. Universal Journal of Mathematics and Applications 5 4 122–129.

IEEE

[1]M. Arslan, M. A. Mustafa, S. Fahad, I. Waheed, and A. Qayyum, “Weighted Ostrowski’s Type Integral Inequalities for Mapping Whose Second Derivative is Bounded”, Univ. J. Math. Appl., vol. 5, no. 4, pp. 122–129, Dec. 2022, doi: 10.32323/ujma.1151207.

ISNAD

Arslan, Muhammad - Mustafa, Muhammad Amir - Fahad, Shah - Waheed, Irfan - Qayyum, Ather. “Weighted Ostrowski’s Type Integral Inequalities for Mapping Whose Second Derivative Is Bounded”. Universal Journal of Mathematics and Applications 5/4 (December 1, 2022): 122-129. https://doi.org/10.32323/ujma.1151207.

JAMA

1.Arslan M, Mustafa MA, Fahad S, Waheed I, Qayyum A. Weighted Ostrowski’s Type Integral Inequalities for Mapping Whose Second Derivative is Bounded. Univ. J. Math. Appl. 2022;5:122–129.

MLA

Arslan, Muhammad, et al. “Weighted Ostrowski’s Type Integral Inequalities for Mapping Whose Second Derivative Is Bounded”. Universal Journal of Mathematics and Applications, vol. 5, no. 4, Dec. 2022, pp. 122-9, doi:10.32323/ujma.1151207.

Vancouver

1.Muhammad Arslan, Muhammad Amir Mustafa, Shah Fahad, Irfan Waheed, Ather Qayyum. Weighted Ostrowski’s Type Integral Inequalities for Mapping Whose Second Derivative is Bounded. Univ. J. Math. Appl. 2022 Dec. 1;5(4):122-9. doi:10.32323/ujma.1151207