پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 610 |
| تعداد مقالات | 9,028 |
| تعداد مشاهده مقاله | 67,082,885 |
| تعداد دریافت فایل اصل مقاله | 7,656,357 |
Hermite-Hadamard type inequality for $\psi$-Riemann-Liouville fractional integrals via preinvex functions | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، شماره 1، خرداد 2022، صفحه 3333-3345 اصل مقاله (424.34 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.21475.2262 | ||
| نویسندگان | ||
| Nidhi Sharma1؛ Shashi Kant Mishra1؛ Abdelouahed Hamdi* 2 | ||
| 1Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India | ||
| 2Department of Mathematics, Statistics and Physics College of Arts and Sciences, Qatar University, P. O. Box 2713, Doha, Qatar | ||
| تاریخ دریافت: 08 مهر 1399، تاریخ بازنگری: 23 شهریور 1400، تاریخ پذیرش: 28 شهریور 1400 | ||
| چکیده | ||
| The main aim of the present paper is to establish a new form of Hermite-Hadamard inequalities using left and right-sided $\psi$-Riemann-Liouville fractional integrals for preinvex functions and present two basic results of $\psi$-Riemann-Liouville fractional integral identities including the first-order derivative of a preinvex function. We derive some fractional Hermite-Hadamard inequalities with the help of these results. Further, we pointed out some applications for special means. | ||
| کلیدواژه‌ها | ||
| Invex sets؛ preinvex functions؛ Hermite-Hadamard inequalities, $\psi$-Riemann-Liouville fractional integrals, Holder's inequality | ||
| مراجع | ||
|
[1] A. Barani, A.G. Ghazanfari and S.S. Dragomir, Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex, J. Inequal. Appl. 2012(1) (2012) 247. [2] A. Ben-Israel and B. Mond, What is invexity?, J. Aust. Math. Soc. Series B. Appl. Math. 28(1) (1986) 1–9. [3] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, Victoria University, Australia, 2000. [4] M. A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl. 80(2) (1981) 545–550. [5] I. I¸scan, Hermite-Hadamard’s inequalities for preinvex functions via fractional integrals and related fractional inequalities, arXiv:1204.0272 (2012). [6] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science Limited, 2006. [7] K. Liu, J. Wang and D. O’Regan, On the Hermite-Hadamard type inequality for ψ-Riemann-Liouville fractional integrals via convex functions, J. Inequal. Appl. 2019(1) (2019) 27. [8] S.K. Mishra and N. Sharma, On strongly generalized convex functions of higher order, Math. Inequal. Appl. 22(1) (2019) 111–121. [9] D.S. Mitrinovi´c and I.B. Lackovi´c, Hermite and convexity, Aequ. Math. 28(3) (1985) 229–232. [10] S.R. Mohan and S.K. Neogy, On invex sets and preinvex functions, J. Math. Anal. Appl. 189 (1995) 901–908. [11] M.A. Noor, Hadamard integral inequalities for product of two preinvex functions, Nonl. A. Forum 14 (2009) 167–173. [12] M.A. Noor, Hermite-Hadamard integral inequalities for log-preinvex functions, J. Math. Anal. Approx. Theory 2(2) (2007) 126–131. [13] M.A. Noor, On Hadamard integral inequalities involving two log-preinvex functions, J. Inequal. Pure. Appl. Math. 8(3) (2007) 1–14. [14] R. Pini, Invexity and generalized convexity, Optim. 22(4) (1991) 513–525. [15] J. Wang and M. Feˇckan, Fractional Hermite-Hadamard Inequalities, De Gruyter, Berlin, 2018. [16] T. Weir and B. Mond, Preinvex functions in multiple objective optimization, J. Math. Anal. Appl. 136 (1998) 29–38. | ||
|
آمار تعداد مشاهده مقاله: 15,726 تعداد دریافت فایل اصل مقاله: 386 |
||