A generalized form of the Hermite-Hadamard-Fejer type inequalities involving fractional integral for co-ordinated convex functions

Document Type : Original paper


Babol Noshirvani University of Technology


Recently, a general class of the Hermit--Hadamard-Fejer inequality on convex functions is studied in [H. Budak, March 2019, 74:29, textit{Results in Mathematics}]. In this paper, we establish a generalization of Hermit--Hadamard--Fejer inequality for fractional integral based on co-ordinated convex functions. Our results generalize and improve several inequalities obtained in earlier studies.


[1] A. Ali, G. Gulshan, R. Hussain, A. Latif, and M. Muddassar, Generalized inequalities of the type of Hermite-Hadamard-Fejér with quasi-convex functions by way of k-fractional derivatives., J. Comput. Anal. Appl. 22 (2017), no. 1, 1208–1219.
[2] A.G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colomb. Math. 28 (1994), no. 1, 7–12.
[3] M. Bombardelli and S. Varošanec, Properties of h-convex functions related to the Hermite-Hadamard-Fejér inequalities, Comput. Math. Appl. 58 (2009), no. 9, 1869–1877.
[4] H. Budak, On Fejér type inequalities for convex mappings utilizing fractional integrals of a function with respect to another function, Results Math. 74 (2019), no. 1, 29.
[5] S.S. Dragomir, On the Hadamard’s inequlality for convex functions on the coordinates in a rectangle from the plane, Taiwanese J. Math. 5 (2001), no. 4, 775–788.
[6] I. Podlubny, Fractional Differential Equations, Academic Press, London, 1999.
[7] M. Z. Sarikaya, E. Set, H. Yaldiz, and N. Basak, Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling 57 (2013), no. 9-10, 2403–2407.
[8] M.Z. Sarikaya, On new Hermite–Hadamard–Fejér type integral inequalities, Stud. Univ. Babes-Bolyai Math. 57 (2012), no. 3, 377–386.
[9] M.Z. Sarıkaya, On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Transforms Spec. Funct. 25 (2014), no. 2, 134–147.
[10] E. Set, I. I¸scan, M. Z. Sarikaya, and M.E. Ozdemir, ¨ On new inequalities of Hermite-Hadamard-Fejér type for convex functions via fractional integrals, Appl. Math. Comput. 259 (2015), 875–881.
[11] H. Yaldız, M.Z. Sarıkaya, and Z. Dahmani, On the Hermite-Hadamard-Fejér type inequalities for co-ordinated convex functions via fractional integrals, Int. J. Optim. Control. Theor. Appl. 7 (2017), no. 2, 205–215.