The main aim of this paper is to give extension and refinement of the Hermite-Hadamard inequality for convex functions via Riemann-Liouville fractional integrals. We show how to relax the convexity property of the function f . Obtained results in this work involve a larger class of functions.

Univariate symmetrization technique has many good properties. In this paper, we adopt the high-dimensional viewpoint, and propose a new symmetrization procedure in arbitrary (convex) polytopes of R with central symmetry. Moreover, the obtained results are used to extend to the arbitrary centrally symmetric polytopes the well-known Hermite-Hadamard inequality for convex functions.

We presented here a refinement of Hermite-Hadamard inequality as a linear combination of its end-points. The problem of best possible constants is closely connected with well known Simpson’s rule in numerical integration. It is solved here for a wide class of convex functions, but not in general. Some supplementary results are also given.

In this paper, we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex. These results are connected with the celebrated Hermite-Hadamard-Fejér type integral inequality. The results presented here would provide extensions of those given in earlier works.

In this paper we extend some estimates of the right hand side of a Hermite-Hadamard type inequality for the product two differentiable functions whose derivatives absolute values are convex. Some natural applications to special weighted means of real numbers are given. Finally, an error estimate for the Simpson’s formula is also addressed.

The results obtained in this paper are a correction of the main results obtained in [14], for which we also give an alternative proof and improvement. We also study some new monotonic conditions under which various generalizations of the Hermite-Hadamard inequality are valid. Furthermore, we give an improvement of the obtained results. Mathematics subject classification (2010): 26A48, 26A51, 26...

In this paper, we establish several weighted inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard Fejér type integral inequality. The results presented here would provide extensions of those given in earlier works. Mathematics Subject Classification (2010): 26D15.

We introduce the notion of strongly h-convex functions (defined on a normed space) and present some properties and representations of such functions. We obtain a characterization of inner product spaces involving the notion of strongly h-convex functions. Finally, a Hermite–Hadamard–type inequality for strongly h-convex functions is given.

In this paper, firstly we have established Hermite–Hadamard-Fejér inequality for fractional integrals. Secondly, an integral identity and some HermiteHadamard-Fejér type integral inequalities for the fractional integrals have been obtained. The some results presented here would provide extensions of those given in earlier works. Mathematics Subject Classification (2010): 26A51, 26A33, 26D10.