On Ostrowski type inequalities via the Taylor's formula

Khan, Asif R.; Nabi, Hira; Pecaric, Josip

doi:10.22075/ijnaa.2023.25999.3185

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	On Ostrowski type inequalities via the Taylor's formula
International Journal of Nonlinear Analysis and Applications
مقاله 213، دوره 14، شماره 1، فروردین 2023، صفحه 2717-2729 اصل مقاله (426.94 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.25999.3185
نویسندگان
Asif R. Khan¹؛ Hira Nabi^* ¹؛ Josip Pecaric²
¹Department of Mathematics, University of Karachi, University Road, Karachi 75270, Pakistan
²Croation Academy of Sciences and Arts, Zagreb, Croatia
تاریخ دریافت: 01 بهمن 1400، تاریخ پذیرش: 25 دی 1401
چکیده
In the present article, our aim is to obtain new Ostrwoski type inequalities by using Taylor's formula with weighted Montgomery identity and the Green's function. The results we acquire containing the identities for the sum $\sum_{i=1}^m p_i f_{1}(\lambda_ i)$ and the integral $\int^{\nu}_{\mu} p(\xi) f_{1}(g(\xi) )\, d\xi$. We also estimate the difference of two weighted integral means for the result obtained by the Taylor formula with weighted Montgomery identity.
کلیدواژه‌ها
Ostrowski inequality؛ Taylor's formula؛ Green's function؛ Integral means

مراجع
[1] A.A. Aljinovi´c, A. Civljak, S. Kovaˇc, J.E. Peˇcari´c and M..R. Penava, ˇ General integral identities and related inequalities, Element, Zagreb, Croatia, 2013. [2] AA. Aljinovic, L. Kvesic and J.E. Pecaric, Weighted Ostrowski type inequalities by Lidstone polynomials, Math. Inequal. Appl. 22 (2019), no. 4, 1271–1282. [3] A.A. Aljinovic, J.E. Pecaric and I. Peric, Estimates of the difference between two weighted integral means via weighted Montgomery identity, Math. Inequal. Appl. 7 (2004), 315–336. [4] G.A. Anastassiou, Ostrowski type inequalities, Proc. Amer. Math. Soc. 123 (1995) 3775–3781. [5] N.S. Barnett, P. Cerone, S.S. Dragomir and A.M. Fink, Comparing two integral means for absolutely continuous mappings whose derivatives are in L∞[a, b] and applications, Comput. Math. Appl. 44 (2002), 241–251. [6] Z. Brady,Inequalities and higher order convexity , arXiv preprint arXiv:1108.5249 (2011). [7] S.I. Butt, N. Mehmood and J.E. Peˇcari´c, New generalizations of Popoviciu type inequalities via new Green functions and Fink’s identity, Trans. A. Razmadze Math. 171 (2017), no. 3, 293–303. [8] N. Irshad, A.R. Khan and M.A. Shaikh, Generalization of weighted Ostrowski inequality with applications in numerical integration, Adv. Inequal. Appl. 2019 (2019) Article 7. [9] A.R. Khan and J.E. Peˇcari´c, Positivity of general linear inequalities for n-convex functions via the Taylor formula using new Green functions, Commun. Optim. Theory 5 (2019), 1–20. [10] A.R. Khan, and J.E. Peˇcari´c, M. Praljak and S. Varoˇsanec, General linear inequalities and positivity, Element, Zagreb, 2017. [11] A.R. Khan, J.E. Peˇcari´c, M. Praljak and S. Varoˇsanec, Positivity of sums for n-convex functions via Taylor’s formula and Green function, Adv. Stud. Contemp. Math. 27 (2017), no. 4, 515–537. [12] L. Kvesi´c, J.E. Peˇcari´c and M.R. Penava, Generalizations of Ostrowski type inequalities via Hermite polynomials, J. Inequal. Appl. 1 (2020), 1–14. [13] M. Matic and J.E. Peˇcari´c, Two-point Ostrowski inequality, Math. Inequal. Appl. 4 (2001), no. 2, 215–221. [14] D.S. Mitrinovi´c, J.E. Peˇcari´c and A.M. Fink, Classical and new inequalities in analysis, ser, Math. Appl. (East European Ser.). Dordrecht: Kluwer Academic Publishers Group, pp. 311–331, 1993. [15] DS. Mitrinovi´c, JE. Peˇcari´c, and AM. Fink, Inequalities for Functions and their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht, 1994. [16] A. Ostrowski, Uber die Absolutabweichung einer differentiebaren Funktion von ihren Integralmittelwert ¨ , Comment. Math. Helvetici 10 (1938), 226–227. [17] J.E. Peˇcari´c, On the Cˇebysev inequality, Sci. Bull. Politeh. Univer. Timi¸soara 25 (1980), no. 39, 5–9. [18] J.E. Peˇcari´c, I. Peri´c and A. Vukeli´c, Estimations of the difference of two integral means via Euler-type identities, Math. Inequal. Appl. 7 (2004), no. 3, 365–378. [19] J.E. Peˇcari´c, A. Peruˇsi´c and K. Smoljak, Generalizations of Steffensen’s inequality by Abel-Gontscharoff polynomial, Khayyam J. Math. 1 (2015), no. 1, 45–61. [20] J.E. Peˇcari´c, F. Proschan and Y.L. Tong, Convex functions, partial orderings, and statistical applications, Academic Press, 1992.
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On Ostrowski type inequalities via the Taylor's formula