In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type via new fractional integral operator associated with the Caputo–Fabrizio derivative are presented. Furthermore, identity for differentiable convex functions of first order is proved. Then, taking into account as an auxiliary result assistance Hölder, power-mean, Young, Jensen inequality, some estimations...

The main target of this paper is to discuss operator Hermite–Hadamard inequality for convex functions, without appealing convexity. Several forms will be presented and some applications including norm mean inequalities shown too.

In this paper we give refinements of converse Jensen’s inequality as well as of the Hermite-Hadamard inequality on time scales. We give mean value theorems and investigate logarithmic and exponential convexity of the linear functionals related to the obtained refinements. We also give several examples which illustrate possible applications for our results. Mathematics subject classification (20...

In this study, the simplex whose vertices are barycenters of the given simplex facets plays an essential role. The article provides an extension of the Hermite-Hadamard inequality from the simplex barycenter to any point of the inscribed simplex except its vertices. A two-sided refinement of the generalized inequality is obtained in completion of this work.

An inequality for convex functions defined on linear spaces is obtained which contains in a particular case a refinement for the second part of the celebrated Hermite-Hadamard inequality. Applications for semi-inner products on normed linear spaces are also provided.

We derive the Levinson type generalization of the Jensen and the converse Jensen inequality for real Stieltjes measure, not necessarily positive. As a consequence, also the Levinson type generalization of the Hermite-Hadamard inequality is obtained. Similarly, we derive the Levinson type generalization of Giaccardi's inequality. The obtained results are then applied for establishing new mean-va...

hold. This double inequality is known in the literature as the Hermite–Hadamard inequality for convex functions. In recent years many authors established several inequalities connected to this fact. For recent results, refinements, counterparts, generalizations and new Hermite-Hadamard’stype inequalities see [1]–[18]. We recall that the notion of quasi-convex function generalizes the notion of ...