The following is the classical Hermite-Hadamard inequality [4, 5]: f ( a+ b 2 ) ≤ 1 b− a (S) ∫ b a f(x)dμ ≤ f(a) + f(b) 2 . which provides estimates of the mean value of a convex function f on [a, b] where μ is the Lebesgue measure on R. This inequality in general, is not valid in the fuzzy context. In this paper, we find necessary and sufficient conditions of Hermite-Hadamard type inequality f...

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.

Some inequalities of Hermite-Hadamard type for h-convex functions de…ned on convex subsets in real or complex linear spaces are given. Applications for norm inequalities are provided as well. 1. Introduction The following inequality holds for any convex function f de…ned on R (1.1) (b a)f a+ b 2 < Z b a f(x)dx < (b a) + f(b) 2 ; a; b 2 R: It was …rstly discovered by Ch. Hermite in 1881 in the j...

An improvement of the Hermite-Hadamard inequality for functions convex on the coordinates is given.

Using the notion of eta-convex functions as generalization of convex functions, we estimate the difference between the middle and right terms in Hermite-Hadamard-Fejer inequality for differentiable mappings. Also as an application we give an error estimate for midpoint formula.

The well-known Hermite-Hadamard integral inequality was established by Hermite at the end of 19th century (see [1]). There are many recent contributions to improve this inequality, please refer to [2,3,4,5,6] and references therein. It is worth noting that there are some interesting results about Hermite-Hadamard inequalities via fractional integrals according to the corresponding integral equa...

In this note we give a simple proof and a new generalization of the Hermite-Hadamard inequality.

In this paper, we present Hermite-Hadamard inequality for p-convex functions in fractional integral forms. we obtain an integral equality and some Hermite-Hadamard type integral inequalities for p-convex functions in fractional integral forms. We give some HermiteHadamard type inequalities for convex, harmonically convex and p-convex functions. Some results presented in this paper for p-convex ...

Keywords: Hermite–Hadamard inequalities Jensen's inequality Xiao–Srivastava–Zhang–Pečarić–Svrtan–Jensen type inequalities Refinements and extensions Convex functions a b s t r a c t The main object of this paper is to give several refinements and extensions of the Hermite–Hadamard and Jensen inequalities in n variables. Relevant connections of the results presented here and the various inequali...

By Hölder's integral inequality, the authors establish some Hermite-Hadamard type integral inequalities for n-times differentiable and geometrically quasi-convex functions.