Hermite–Hadamard–Fejér type inequalities involving generalized fractional integral operators
- 10 Downloads
Since the so-called Hermite–Hadamard type inequalities for convex functions were presented, their generalizations, refinements, and variants involving various integral operators have been extensively investigated. Here we aim to establish several Hermite–Hadamard–Fejér type inequalities for symmetrized convex functions and Wright-quasi-convex functions with a weighted function symmetric with respect to the midpoint axis on the interval involving the known generalized fractional integral operators. We also point out that certain known inequalities are particular cases of the results presented here.
KeywordsConvex function Quasi-convex function Symmetrized convex function Wright-quasi-convex functions Hermite–Hadamard type inequalities Generalized fractional integral operators Hermite–Hadamard–Fejér type inequalities
Mathematics Subject Classification26A33 26D10 26D15 33B20
This research is supported by Ordu University Scientific Research Projects Coordination Unit (BAP). Project Number: B-1809.
Compliance with ethical standards
Human participants or animals rights
This article does not contain any studies with human participants or animals performed by any of the authors.
Conflict of interest
Erhan Set declares that he has no conflict of interest. Junesang Choi declares that he has no conflict of interest. E. Aykan Alan declares that he has no conflict of interest.
- 5.Dragomir, S.S. 2017. Some inequalities of Hermite-Hadamard type for symmetrized convex functions and Riemann-Liouville fractional integrals. RGMIA Res. Rep. Coll 20: 15. (Art. 46).Google Scholar
- 6.Dragomir, S.S., and C.E.M. Pearce. 2000. Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs. Footscray: Victoria University.Google Scholar
- 9.Fejér, L. 1906. Uberdie Fourierreihen \(\prod\). Math. Naturwise. Anz Ungar. Akad., Wiss 24: 369–390. (in Hungarian).Google Scholar
- 10.Gorenflo, R., and F. Mainardi. 1997. Fractional Calculus: Integral and Differential Equations of Fractional Order, 223–276. Wien: Springer.Google Scholar
- 11.İşcan, İ. 2014 Hermite-Hadamard-Fejér type inequalities for convex functions via fractional integrals, arXiv preprint arXiv:1404.7722.
- 16.Set, E., A.O. Akdemir, and B. Çelik. On Generalization of Fejér type inequalities via fractional integral operator, Filomat (accepted).Google Scholar
- 19.Set, E., and B. Çelik. On generalizations related to the left side of Fejér’s inequality via fractional integral operator, Miskolc Mathematical Notes, (accepted).Google Scholar
- 20.Set, E., J. Choi, and B. Çelik. 2017. Certain Hermite-Hadamard type inequalities involving generalized fractional integral operators. RACSAM. https://doi.org/10.1007/s13398-017-0444-1.
- 21.Set, E., J. Choi, and A. Gözpınar. 2017. Hermite-Hadamard type inequalities for the generalized \(k\)-fractional integral operators. Journal of Inequalities and Application. https://doi.org/10.1186/s13660-017-1476-y (Article ID 206).
- 26.Set, E., M.A. Noor, M.U. Awan, and A. Gözpınar. 2017. Generalized Hermite-Hadamard type inequalities involving fractional integral operators. Journal of Inequalities and Applications. https://doi.org/10.1186/s13660-017-1444-6 (Article ID 169).
- 30.Yaldız, H., and M.Z. Sarıkaya. On the Hermite-Hadamard type inequalities for fractional integral operator, Preprint.Google Scholar
- 31.Usta, F., H. Budak, M.Z. Sarıkaya, and E. Set. On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators. Filomat (accepted).Google Scholar