In this paper, we obtain some new weighted Hermite–Hadamard-type inequalities for (n+2)?convex functions by utilizing generalizations of Steffensen’s inequality via Taylor’s formula.

In the paper, we study dynamic h-convexity for interval valued functions. Some generalizations of Jensen’s inequality in analysis h-convex functions on time scales are proved paper. seek applications generalized inequality, Hermite-Hadamard type inequalities established. Further discrete analogues newly results also presented numerical examples provided to check validity results.

In this note, we obtain a reverse version of the integral Hardy inequality on metric measure spaces. Moreover, give necessary and sufficient conditions for weighted to be true. The main tool in our proof is continuous Minkowski inequality. addition, present some consequences obtained homogeneous groups, hyperbolic spaces Cartan-Hadamard manifolds.

In this paper, by applying the new and improved form of Hölder’s integral inequality called Hölder—Íşcan three inequalities Hermite—Hadamard Hadamard type for (h, d)—convex functions have been established. Various special cases including classes instance, h—convex, s—convex function Breckner Godunova—Levin—Dragomir strong versions aforementioned types convex identified. Some applications to err...

We establish some results concerning P{functions from the standpoint of abstract convexity. In particular, we show that the set of all P{functions on a segment is the least set closed under pointwise sum, supremum and convergence and containing the class of all nonnegative quasiconvex functions on that segment. Further, generalizations are derived of a recent inequality of Hadamard type for P{f...

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we give a simple proof and a new generalization of the Hermite-Hadamard inequality for operator convex functions.

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.

X. Zhan has conjectured that the spectral radius of the Hadamard product of two square nonnegative matrices is not greater than the spectral radius of their ordinary product. We prove Zhan’s conjecture, and a related inequality for positive semidefinite matrices, using standard facts about principal submatrices, Kronecker products, and the spectral radius.