In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.

In this paper, we obtain new generalization of Hermite-Hadamard inequalities via generalized fractional integrals defined by Sarikaya and Ertu?ral in [12]. We establish some midpoint trapezoid type for functions whose first derivatives absolute value are convex involving integrals.

Abstract We introduce new time scales on $\mathbb{Z}$ Z . Based this, we investigate the discrete inequality of Hermite–Hadamard type for convex functions. Finally, improve our result to fractional functions involving left nabla and right delta sums.

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.