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Kashuri, Artion, Ali, Muhammad, Abbas, Mujahid, BUDAK, Huseyin. (1398). New inequalities for generalized m-convex functions via generalized fractional integral operators and their applications. هنرهای کاربردی, 10(2), 275-299. doi: 10.22075/ijnaa.2019.18455.2014
Artion Kashuri; Muhammad Aamir Ali; Mujahid Abbas; Huseyin BUDAK. "New inequalities for generalized m-convex functions via generalized fractional integral operators and their applications". هنرهای کاربردی, 10, 2, 1398, 275-299. doi: 10.22075/ijnaa.2019.18455.2014
Kashuri, Artion, Ali, Muhammad, Abbas, Mujahid, BUDAK, Huseyin. (1398). 'New inequalities for generalized m-convex functions via generalized fractional integral operators and their applications', هنرهای کاربردی, 10(2), pp. 275-299. doi: 10.22075/ijnaa.2019.18455.2014
Kashuri, Artion, Ali, Muhammad, Abbas, Mujahid, BUDAK, Huseyin. New inequalities for generalized m-convex functions via generalized fractional integral operators and their applications. هنرهای کاربردی, 1398; 10(2): 275-299. doi: 10.22075/ijnaa.2019.18455.2014

New inequalities for generalized m-convex functions via generalized fractional integral operators and their applications

International Journal of Nonlinear Analysis and Applications
مقاله 40، دوره 10، شماره 2، اسفند 2019، صفحه 275-299    اصل مقاله (508.66 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.18455.2014
نویسندگان
Artion Kashuri* 1؛ Muhammad Aamir Ali2؛ Mujahid Abbas3؛ Huseyin BUDAK4
1Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, 9400, Vlora, Albania
2Department of Mathematics Government College University Faisalabad Sahiwal Campus, Pakistan
3Department of Mathematics, Government College University, Lahore 54000, Pakistan and Department of Mathematics and Applied, Mathematics, University of Pretoria, Lynnwood road, Pretoria 0002, South Africa
4Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce, Turkey
تاریخ دریافت: 19 مرداد 1398،  تاریخ بازنگری: 11 آبان 1398،  تاریخ پذیرش: 16 آبان 1398 
چکیده
In the present work, we prove a parametrized identity for a differentiable function via generalized integral operators. By applying the established identity and the new so-called generalized m-convex function, some generalized trapezium, Ostrowski and Simpson type integral inequalities have been discovered. Various special cases have been studied as well. Some applications of the present results to special means and new error estimates for the trapezium and midpoint quadrature formula have been investigated. It is hoped that the methods and techniques of this paper could further stimulate the research conducted in the field of integral inequalities.
کلیدواژه‌ها
Trapezium inequality؛ Ostrowski inequality؛ Simpson inequality؛ convexity؛ general fractional integrals
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