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

Year 2022, Volume: 5 Issue: 4, 122 - 129, 29.12.2022

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

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

Cited By: 1

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

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Project Number

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Thanks

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References

• [1] A. Ostrowski. Uber die absolutabweichung einer differentienbaren funktionen von ihren Integralmittelwert, Comment. Math. Helv., 10 (1938), 226–227.
• [2] P. Cerone, A new Ostrowski type inequality involving integral means over end intervals, Tamkang J. Math., 33(2) (2002), 109-118.
• [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.
• [5] A. Qayyum, A weighted Ostrowski Gruss type inequality for twice differentiable mappings and applications, Int. J. Math. Comp., 1(8) (2008), 63-71.
• [6] A. Qayyum, M. Shoaib, M. A. Latif, A generalized inequality of Ostrowski type for twice differentiable bounded mappings and applications, Appl. Math. Sci., 8(38) (2014), 1889-1901.
• [7] A. Qayyum, M. Shoaib, A. E. Matouk, M. A. Latif, On new generalized Ostrowski type integral inequalities, Abstr. Appl. Anal., 2014 (2014), Article ID: 275806, 8 pages.
• [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.
• [10] N. S. Burnett, P. Cerone, S. S. Dragomir, J. Roumeliotis, A. Sofo, A survey on Ostrowski type inequalities for twice differentiable mappings and applications, Inequality Theory and Applications, 1 (2001), 24-30.
• [11] H. Budak, M. Z. Sarıkaya, A. Qayyum, New refinements and applications of Ostrowski type inequalities for mappings whose nth derivatives are of bounded variation, TWMS J. Appl. Eng. Math., 11(2) (2021), 424-435.
• [12] J. Nasir, S. Qaisar, S. I. Butt, A. Qayyum, Some Ostrowski type inequalities for mappings whose second derivatives are preinvex function via fractional integral operator, AIMS Mathematics, 7(3) (2021), 3303–3320.
• [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.
• [16] J. Amjad, A. Qayyum, S. Fahad, M. Arslan, Some new generalized Ostrowski type inequalities with new error bounds, Innov. J. Math., 1 (2022), 30–43.
• [17] S. Dragomir, J. Roumeliotis, An inequality of Ostrowski type for mappings whose second derivatives are bounded and applications, RGMIA Research Report Collection, 1(1) (1998), 33-39.