The authors shall discuss Heinz inequalities involving Riemann-Liouville fractional integrals for certain unitarily invariant norms. By using the convexity of function and fractional Hermit-Hadamard integral inequality, some refinements of Heinz inequalities are derived.

The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovich inequalities for positive real numbers. We also prove a generalization of Fiedler’s inequality.

In this paper we obtain some Hadamard type inequalities for triple integrals. The results generalize those obtained in (S.S. DRAGOMIR, On Hadamard’s inequality for the convex mappings defined on a ball in the space and applications, RGMIA (preprint), 1999).

The main results of this paper offer sufficient conditions in order that an approximate lower Hermite–Hadamard type inequality implies an approximate Jensen convexity property. The key for the proof of the main result is a Korovkin type theorem.

The goal of this study is to create new variations the well-known Hermite–Hadamard inequality (HH-inequality) for preinvex interval-valued functions (preinvex I-V-Fs). We develop several additional inequalities class whose product I-V-Fs. findings described here would be generalizations those found in previous studies. Finally, we obtain Hermite–Hadamard–Fejér with support functions. Some and c...

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...

Abstract In this paper, we obtain new Hermite–Hadamard-type inequalities for r -convex and geometrically convex functions and, additionally, some by using the Hölder–İşcan integral inequality an improved power-mean inequality.

In this paper we introduce the concept of geometrically quasiconvex functions on the co-ordinates and establish some Hermite-Hadamard type integral inequalities for functions defined on rectangles in the plane. Some  inequalities for product of two geometrically quasiconvex functions on the co-ordinates are considered.

Recently, new developments of the theory and applications of dynamic derivatives on time scales were made. The study provides an unification and an extension of traditional differential and difference equations and, in the same time, it is a unification of the discrete theory with the continuous theory, from the scientific point of view. Moreover, it is a crucial tool in many computational and ...

equality holds in either side only for the affine functions (i.e., for the functions of the form mx+ n). The middle point (a + b)/2 represents the barycenter of the probability measure 1 b−adx (viewed as a mass distribution over the interval [a, b]), while a and b represent the extreme points of [a, b]. Thus the Hermite-Hadamard inequality could be seen as a precursor of Choquet’s theory. See [...