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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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