Hermite–Hadamard inequality is a double that provides an upper and lower bounds of the mean (integral) convex function over certain interval. Moreover, convexity can be characterized by each two sides this inequality. On other hand, it well known twice differentiable convex, if only admits nonnegative second-order derivative. In paper, we obtain characterization class functions (including funct...

In this paper, we extend some estimates of a Hermite-Hadamard type inequality for functions whose absolute values the first derivatives are $p$-convex. By means obtained inequalities, bound involving beta and hypergeometric derived as applications. Also, suggest an upper error in numerical integration $p$-convex via composite trapezoid rule.

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.

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.