New Refinements of Hadamard Integral inequlaity via k-Fractional Integrals for p-Convex Function

Abstract

In this study, we use k-fractional integrals to establish some new integral inequalities for p- convex function. These integral inequalities includes some new estimations for Hadamard inequality via k-fractional integrals.

Keywords

• Hermite- Hadamard inequality
• k-fractional integrals
• p-functions

Kaynakça

1. Belarbi S, Dahmani Z. On some new fractional integral inequalities, J. Ineq. Pure & Appl. Math., 10(3) (2009), Art. 86.
2. Budak H, Usta F, Sar¨kaya MZ, ÷zdemir ME. On generalization of midpoint type inequalities with generalized fractional integral operators, RACSAM, https://doi.org/10.1007/s13398- 018-0514-z
3. Dahmani Z. New inequalities in fractional integrals, International Journal of Nonlinear Science, 9(4) (2010), 493-497.
4. Dahmani Z, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal 6 M. E. ÷ZDEM IR
5. Dahmani Z, Tabharit L, Taf S. Some fractional integral inequalities, Nonl. Sci. Lett. A., 1(2) (2010), 155-160.
6. Dahmani Z, Tabharit L, Taf S. New generalizations of Gruss inequality using RiemannLiouville fractional integrals, Bull. Math. Anal. Appl., 2(3) (2010), 93-99.
7. Dragomir SS, Pearce CEM. Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University,2000. ONLINE: http://rgmia. vu. edu.au/monographs.
8. Gorenáo R, F. Mainardi F. Essentials of fractional calculus, (2000).

9. Oldham K, J. Spanier J. The fractional calculus, Academic Press, New York- London, (1974).
10. ÷zdemir ME, Y¨ld¨z «. An Ostrowski type inequality for derivatives of q-th power of s-convex functions via fractional integrals, Georgian Math. J. 21(4) (2014), 491ñ498.
11. ÷zdemir ME, Dragomir SS, Y¨ld¨z «. The Hadamard inequality for convex function via fractional integrals, Acta Math. Sci., 33B (5) (2013), 1293ñ1299.
12. M. Emin ÷ZDEMIR, Hemen Dutta, Ahmet OCAK AKDEM · IR, New ReÖnements for · Hadamard inequality via k- Riemann ñLiouville fractional integral operators, Mathematics in Engineering , Science and Aerospace, vol.11, No.2, pp. 323-332, 2020, CSPó Cambridge,UK;1&S-Florida,USA, 2020.
13. Podlubny I. Fractional diferential equations, Academic Prss, San Diego, (1999).
14. Sar¨kaya MZ, Set E, Yald¨z H, Ba¸sak N. Hermite-Hadamardís inequalities for fractional integrals and related fractional inequalities, Math. and Comput. Mod., 57(9-10) (2013), 2403-2407.
15. Set E, ÷zdemir ME, Korkut N. Certain new Hermite-Hadamard type inequalities for convex functions via fractional integrals, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1)(2019), 61-69.
16. Wang J, L¨X, Feµckan M, Zhou Y. Hermite Hadamard type inequalities for Riemann Liouville fractional integrals via two kinds of convexity, Appl. Anal., 92 (2003), 2241-2253.
17. Y¨ld¨z «, ÷zdemir ME ÷nalan HK. Fractional integral inequalities for di§ erent functions, New Tren. Math. Sci., 2 (2015), 110-117.
18. Y¨ld¨z «, ÷zdemir ME, Sar¨kaya MZ. New generalizations of Ostrowski-Like type inequalities for fractional integrals, Kyungpook Math. J., 56 (2016), 161-172.