In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.

Hermite-Hadamard inequality is one of the fundamental applications of convex functions in Theory of Inequality. In this paper, Hermite-Hadamard inequalities for $mathbb{B}$-convex and $mathbb{B}^{-1}$-convex functions are proven.

The classical Hermite-Hadamard inequality characterizes the continuous convex functions of one real variable. The aim of the present paper is to give an analogous characterization for functions of a vector variable. 1. The Hermite-Hadamard inequality In a letter sent on November 22, 1881, to the journal Mathesis (and published there two years later), Ch. Hermite [10] noted that every convex fun...

Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named [Formula: see text]-Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.

in this paper we establish several polynomials similar to bernstein's polynomials and several refinements of  hermite-hadamard inequality for convex functions.

In this paper we establish several polynomials similar to Bernstein's polynomials and several refinements of  Hermite-Hadamard inequality for convex functions.

In this paper we introduce operator preinvex functions and establish a Hermite–Hadamard type inequality for such functions. We give an estimate of the right hand side of a Hermite–Hadamard type inequality in which some operator preinvex functions of selfadjoint operators in Hilbert spaces are involved. Also some Hermite–Hadamard type inequalities for the product of two operator preinvex functio...

In this paper, we obtain Jensen’s inequality for GG-convex functions. Also, we get in- equalities alike to Hermite-Hadamard inequality for GG-convex functions. Some examples are given.

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.

Keywords: m-convex functions Hermite–Hadamard inequalities Hölder inequality Power-mean inequality a b s t r a c t In this paper we give some estimates to the right-hand side of Hermite–Hadamard inequality for functions whose absolute values of second derivatives raised to positive real powers are m-convex.