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Ostrowski type inequalities via $(\alpha,\beta,\gamma,\delta)$-convex function | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 15، دوره 16، شماره 12، اسفند 2025، صفحه 187-203 اصل مقاله (453.78 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.24568.2771 | ||
| نویسندگان | ||
| Ali Hassan* 1؛ Asif R. Khan2 | ||
| 1Shah Abdul Latif University, Department of Mathematics, Khairpur-66020, Pakistan | ||
| 2University of Karachi, Faculty of Science, Department of Mathematical Sciences, University Road, Karachi-75270, Pakistan | ||
| تاریخ دریافت: 26 شهریور 1400، تاریخ بازنگری: 02 مهر 1400، تاریخ پذیرش: 25 آذر 1400 | ||
| چکیده | ||
| In this paper, we are introducing very first time the class of $(\alpha,\beta,\gamma,\delta)-$ convex (concave) function in mixed kind, which is the generalization of many classes of functions given in [2, 3, 4, 15, 16, 17]. We would like to state the well-known Ostrowski inequality via generalized Montgomery identity [14] for $(\alpha,\beta,\gamma,\delta)-$ convex (concave) function in mixed kind. In addition, we establish some Ostrowski-type inequalities for the class of functions whose derivatives in absolute values at certain powers are $(\alpha,\beta,\gamma,\delta)$-convex (concave) functions in mixed kind by using different techniques including Holder's inequality [27] and power mean inequality [26]. Also, various established results would be captured as special cases. Moreover, some applications in terms of special means would also be given. | ||
| کلیدواژهها | ||
| Ostrowski inequality؛ Generalized Montgomery identity؛ convex functions؛ special means | ||
| مراجع | ||
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[1] M. Alomari, M. Darus, S.S. Dragomir, and P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Appl. Math. Lett. 23 (2010), 1071—1076. [2] A. Arshad and A.R. Khan, Hermite-Hadamard-Fejer type integral inequality for s−p−convex functions of several kinds, TJMM 11 (2019), no. 2, 25–40. [3] E.F. Beckenbach, Convex functions, Bull. Amer. Math. Soc. 54 (1948), 439–460. [4] W.W. Breckner, Stetigkeitsaussagen fur eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Raumen, Publ. Inst. Math. 23 (1978), no. 37, 13–20. [5] P. Cerone and S.S. Dragomir, Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions, Demon. Math. 37 (2004), no. 2, 299–308. [6] S.S. Dragomir, A functional generalization of Ostrowski inequality via Montgomery identity, Acta Math. Univ. Comenianae 84 (2015), no. 1, 63–78. [7] S.S. Dragomir, Integral inequalities of Jensen type for λ-convex functions, Mate. Vesnik 68 (2016), no. 1, 45–57. [8] S.S. Dragomir, Inequalities of Jensen type for η−convex functions, Fasciculi Math. 5 (2015), 35–52. [9] S.S. Dragomir, A companion of Ostrowski’s inequality for functions of bounded variation and applications, Int. J. Nonlinear Anal. Appl. 5 (2014), 89–97. [10] S.S. Dragomir, On the Ostrowski’s integral inequality for mappings with bounded variation and applications, Math. Inequal. Appl. no. 4(1), (2001), 59–66. [11] S.S. Dragomir, Refinements of the generalised trapezoid and Ostrowski inequalities for functions of bounded variation, Arch. Math. 91 (2008), no. 5, 450–460. [12] S.S. Dragomir and N.S. Barnett, An Ostrowski type inequality for mappings whose second derivatives are bounded and applications, J. Indian Math. Soc. (N.S.) 66 (1999), no. 4, 237–245. [13] S.S. Dragomir, P. Cerone, N.S. Barnett, and J. Roumeliotis, An inequality of the Ostrowski type for double integrals and applications for Cubature formulae, RGMIA Res. Rep. Coll. 2 (1999), no. 6, 1–16. [14] S. S. Dragomir, P. Cerone and J. Roumeliotis, A new generalization of Ostrowski integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means, Appl. Math. Lett. 13 (2000), 19–25. [15] S.S. Dragomir, J. Pecaric, and L. Persson, Some inequalities of Hadamard type, Soochow J. Math. 21 (1995), no. 3, 335–341. [16] A. Ekinci, Klasik esitsizlikler yoluyla konveks Fonksiyonlar icin integral esitsizlikler, Ph.D. Thesis, Thesis ID: 361162 in tez2.yok.gov.tr Ataturk University, 2014. [17] E.K. Godunova and V.I. Levin, Inequalities for functions of a broad class that contains convex, monotone and some other forms of functions, Numer. Math. Math. Phys. 166 (1985), 138–142. [18] N. Irshad, A.R. Khan, and A. Nazir, Extension of Ostrowski type inequality via moment generating function, Adv. Inequal. Appl. 2, (2020), 1–15. [19] N. Irshad, A.R. Khan, and M.A. Shaikh, Generalization of weighted Ostrowski inequality with applications in numerical integration, Adv. Ineq. Appl. 7 (2019), 1–14. [20] N. Irshad, A.R. Khan, and M.A. Shaikh, Generalized weighted Ostrowski-Gruss type inequality with applications, Glob. J. Pure Appl. Math. 15 (2019), no. 5, 675–692. [21] N. Irshad and A.R. Khan, On weighted Ostrowski Gruss inequality with applications, TJMM, 10 (2018), no. 1, 15–22. [22] N. Irshad and A.R. Khan, Generalization of Ostrowski inequality for differentiable functions and its applications to numerical quadrature rules, J. Math. Anal. 8 (2017), no. 1, 79–102. [23] D.S. Mitrinovic, J.E. Pecaric, and A.M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives Kluwer Academic, Dordrecht, 1991. [24] M.A. Noor and M.U. Awan, Some integral inequalities for two kinds of convexities via fractional integrals, TJMM, 5 (2013), 129 – 136. [25] A.M. Ostrowski, Uber die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10 (1938), 226–227. [26] Z.G. Xiao, and A.H. Zhang, Mixed power mean inequalities, Res. Commun. Inequal. no. 8 (2002), no. 1, 15—17. [27] X. Yang, A note on Holder inequality, Appl. Math. Comput. 134 (2003), 319–322. | ||
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