New Developments in Ostrowski's Type Inequalities by Using 13-Step Quadratic Kernel

Authors

DOI:

https://doi.org/10.22452/mjs.vol44no4.9

Keywords:

Ostrowski Inequalities, Numerical Integration, Quadratic Kernel, Cumulative Distributive Functions

Abstract

The Ostrowski inequality has recently been widely recognized as a powerful mathematical tool for modeling and analysing many physical and real-world events. This inequality has been applied across diverse mathematical fields, including complex analysis, numerical analysis, functional analysis, and stochastic analysis. The purpose of this paper is to develop  Ostrowski's type integral inequalities by using a special type of 13-steps quadratic kernel. The incorporation of this new kernel gives some new error bounds for various quadrature rules. Applications for cumulative distributive functions are also discussed.

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References

A. Guessab and G. Schmeisser, Sharp integral inequalities of the Hermite-Hadamard type, Journal of Approximation Theory. (2002) 115(2):260-288.

A. Munir, M. Vivas-Cortez, A. Qayyum, H. Budak, I. Faiz and S. S. Supadi, Some new fractional corrected Euler-Maclaurin type inequalities for function whose second derivatives are s-convex function. Mathematical and Computer Modelling of Dynamical Systems, (2024), 30(1), 543–566.

A. Munir, A. Qayyum, L. Rathour, G. Atta, S. S. Supadi and U. Ali, A study on Milne-type inequalities for a specific fractional integral operator with applications, Korean J. Math. (2024), 32 No. 2, pp. 297–314.

A. Ostrowski. Über die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert.Comment.Math.Helv. (1938) 10,226-227.

A. Qayyum, M. Shoaib, I. Faye, On New Weighted Ostrowski Type inequalities Involving Integral Means Over End Intervals and Application, Turkish Journal of Analysis and Number Theory, (2015) Vol.3, No.2, 61-67.

A. Qayyum, M. Shoaib and I. Faye, Some New Generalized Results on Ostrowski Type Integral Inequalities With Application, Journal of computational analysis and applications. (2015) vol.19,No.4.

A. Qayyum, M. Shoaib, S. Erden, On Generalized fractional Ostrowski type inequalities for higher order derivatives, communication in mathematical modeling and applications, (2019) vol.4 (2).

F. Zafar, H. Kalsoom and N. Hussain, Some inequalities of Hermite-Hadamard type for n-times di erentiable (rho,m)- geometrically convex functions, Journal of Nonlinear Science and Applications. (2015) 8 201-217.

H. Budak, M. Z. Sarikaya, A. Qayyum, New Refinements And Applications Of Ostrowski Type Inequalities For Mappings Whose nth Derivatives Are Of Bounded Variation, TWMS J. App. Eng. Math. (2021) Vol.11, No.2.

Junjua, M.-u.-D.; Qayyum,A.; Munir, A.; Budak, H.; Saleem,M.M.; Supadi, S.S. A Study of SomeNew Hermite–Hadamard Inequalitiesvia Specific Convex Functions withApplications. Mathematics 2024, 12,478.

M.M. Jamei and N. Hussain, On orthogonal polynomials and quadrature rules related to the second kind of Beta distribution,Journal of Inequalities and Applications. (2013) 2013:157.

M. Maaz, M. Muawwaz, U. Ali, M. D. Faiz, E. Abdulrehman and A. Qayyum, New Extension in Ostrowski’s Type Inequalities by Using 13-Step Linear Kernel, Advances in Analysis and Applied Mathematics, (2024), 1(1), 55–67.

M. Muawwaz, M. Maaz, A. Qayyum, M. Ahmad, M. D. Faiz, and A. Mehboob, Innovative Ostrowski’s Type Inequalities Based on Linear Kernel and Applications, Palestine Journal of Mathematics, (2025), 14(1), 802–812.

Muhammad Muawwaz, Muhammad Maaz and Ather Qayyum, Ostrowski’s type inequalities by using the modified 2-step linear kernel, Eur. J. Math. Appl. (2024) 4, Article ID 6.

M.W. Alomari, A companion of Ostrowski's inequality with applications. Transylvanian Journal of Mathematics and Mechanics. (2011) 3:9-14.

M.W. Alomari, A companion of ostrowski's inequality for mappings whose rst derivatives are bounded and applications numerical integration, Kragujevac Journal of Mathematics. (2012) 36:77-82.

W. Liu, Y. Zhu and J. Park, Some companions of perturbed Ostrowski-type inequalities based on the quadratic kernel function with three sections and applications, Journal of Inequalities and Applications. (2013):226.

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Published

31-12-2025

How to Cite

Muawwaz, M., Maaz, M., Qayyum, A., Suzlin Supadi, S. ., Ali, U., & Danial Faiz, M. (2025). New Developments in Ostrowski’s Type Inequalities by Using 13-Step Quadratic Kernel. Malaysian Journal of Science (MJS), 44(4), 92–101. https://doi.org/10.22452/mjs.vol44no4.9

Issue

Vol 44 No 4 (2025): December 2025

Section

Original Articles

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