Certain New Hermite-Hadamard Type Inequalities for Convex Functions Via Fractional Integrals

Yıl 2019, Cilt: 68 Sayı: 1, 61 - 69, 01.02.2019

Erhan Set M. Emin Özdemir Necla Korkut

https://doi.org/10.31801/cfsuasmas.443617

Cited By: 2

Öz

The object of this paper is to obtain certain Hermite-Hadamard type integral inequalities involving general class of fractional integral operators and the fractional integral operators with exponential kernel by using harmonically convex functions

Anahtar Kelimeler

Harmonically convex function, Hermite-Hadamard inequality, fractional integral operator

Kaynakça

• Agarwal, R.P., Luo M.J. and Raina, R.K., On Ostrowski type inequalities, Fasciculi Mathematici, 204 (2016), 5-27.
• Hermite, C., Sur deux limites d'une integrale definie, Mathesis, 3, 82 (1883).
• İşcan, İ., Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat. Doi: 10.15672/HJMS.2014437519.
• İşcan, İ. and Wu, S., Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Applied Mathematics and Computation 238, (2014) 237-244 .
• Kirane, M. and Torebek B.T., Hermite-Hadamard, Hermite-Hadamard-Fejer, Dragomir-Agarwal and Pachpatte type inequalities for convex functions via fractional integrals, arXiv:1701.00092v1 [math.FA] (2016).
• Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam (2006).
• Raina, R.K., On generalized Wright's hypergeometric functions and fractional calculus operators, East Asian Math. J., 21(2) (2005), 191-203.
• Sarıkaya, M.Z., Set, E., Yaldız, H. and Başak, N., Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model. 57(9-10), (2013) 2403-2407.
• Set, E. and Gözpınar, A., Some new inequalities involving generalized fractional integral operators for several class of functions, AIP Conference Proceedings, 1833, 020038 (2017); doi: 10.1063/1.4981686.
• Set, E. and Gözpınar, A., Hermite-Hadamard Type Inequalities for convex functions via generalized fractional integral operators, Topol. Algebra Appl, 5 (2017) 55--62.
• Set, E., Akdemir, A.O. and Çelik, B., On Generalization of Fejér Type Inequalities via fractional integral operator, ResearchGate, https://www.researchgate.net/publication/311452467.
• Set, E. and Çelik, B., On generalization related to the left side of Fejér's inequalites via fractional integral operator, ResearchGate, https://www.researchgate.net/publication/311651826.
• Set, E., Choi, J. and Çelik, B., Certain Hermite-Hadamard type inequality involving generalized fractional integral operators, RACSAM, Doi: 10.1007/s13398-017-0444-1.
• Usta, F., Budak, H., Sarıkaya M.Z. and Set, E., On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators, Filomat, accepted.
• Yaldız H. and Sarıkaya, M.Z., On the Hermite-Hadamard type inequalities for fractional integral operator, ResearchGate, https://www.researchgate.net/publication/309824275.