Abstract
In the present work, it is obtained some results concerning the integral inequality of Hermite-Hadamard, and others related to it, using η−convex functions and the fractional integral operator defined by R.K. Raina.
References
Agarwal, R.P.; Luo, M-J.; Raina, R.K. (2016) “On Ostrowski type inequalities”, Fasciculi Mathematici 56(1): 5–27.
Bai, R.; Qi, F.; Xi, B. (2013) “Hermite-Hadamard type inequalities for them− and (α, m)−logarithmically convex functions”, Filomat 27(1): 1–7.
Dragomir, S.S.; Pecaric, J.; Persson; L. (1995) “Some inequalities of Hadamard type”, Soochow Journal of Mathematics 21(3): 335–341.
Dragomir, S.S.; Pearce, C.E.M. (2002) Selected Topics on Hermite Hadamard Inequalities and Applications. RGMIA Monographs, Victoria University.
Gordji, M.E.; Delavar, M.R.; Dragomir, S.S. (2015) “Some inequality related to η-convex function”, Preprint, RGMIA Research Report Collection.
Eshaghi, M.; Dragomir, S.S.; Delavar, M.R. (2015) “An inequality related to η−convex functions”, International Journal of Nonlinear Analysis and Applications 6(2): 26–32.
Hadamard, J. (1893) “Etude sur les propriétés des fonctions entières et en particulier d’une fonction considérée par Riemann”, Journal de Mathématiques Pures et Appliquées 58: 171–216.
Iqbal, M.; Iqbal, M.; Nazeer, K. (2015) “Generalization of inequalities analogous to Hermite-Hadamard inequality via fractional integrals”, Bulletin of the Korean Mathematical Society 52(3): 707–716.
Khan, M.A.; Khurshid, Y.; Ali, T. (2017) “Hermite-Hadamard inequality for fractional integrals via η−convex functions”, Acta Mathematica Universitatis Comenianae 86(1): 153–164.
Latif, M.A.; Alomari, M. (2009) “On Hadmard type inequalities for hconvex functions on the co-ordinates”, International Journal of Mathematical Analysis 3(33): 1645–1656.
Özdemir, M.E.; Akdemir, A.O.; Set, E. (2016) “On (h, m)−Convexity and Hadamard Type Inequalities”, Transylvanian Journal of Mathematics and Mechanics 8(1): 51–58.
Raina, R.K. (2005) “On Generalized Wright’s Hypergeometric Functions and Fractional Calculus Operators", East Asian Mathematics Journal 21(2): 191–203.
Sarikaya, M.Z.; Set, E.; Yaldiz, H.; Basak, N. (2013) “Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities”, Mathematical and Computer Modelling 57(9-10): 2403–2407.
Set, E.; Çelik, B.; Akdemir, A.O. (2017) “Some new Hermite-Hadamard type inequalities for quasi-convex functions via fractional integral operator”, in A.O. Akdemir; A. Ekinci; I. Han; E. Set; F. Dadasoglu; K. Karagoz & A. Oztekin (Eds.) American Institute of Physics Conference Proceedings, AIP Publishing, Antalya, Turkey: 1–8.