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.

In this paper an inequality of Hadamard type for convex functions defined on a disk in the plane is proved. Some mappings naturally connected with this inequality and related results are also obtained.

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

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...

This doubly inequality is known in the literature as Hermite-Hadamard integral inequality for convex mapping.We note that Hadamard’s inequality may be regarded as a refinement of the concept of convexity and it follows easily from Jensen’s inequality. For several recent results concerning the inequality (1) we refer the interested reader to [3,5,6,8,9,11,18,21,22] and the references cited there...

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

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...

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.

Worldline quantum inequalities provide lower bounds on weighted averages of the renormalised energy density of a quantum field along the worldline of an observer. In the context of real, linear scalar field theory on an arbitrary globally hyperbolic spacetime, we establish a worldline quantum inequality on the normal ordered energy density, valid for arbitrary smooth timelike trajectories of th...