In this paper, we present a weighted version of the Hermite–Hadamard inequality for convex functions on time scales, with weights that are allowed to take some negative values, these are the Steffensen–Popoviciu and the Hermite–Hadamard weights. We also present some applications of this inequality.

Sharp lower and upper bounds for quasiconvex moments of generalized order statistics are proven by the use of the rearranged Moriguti’s inequality. Even in the second moment case, the method yields improvements of known quantile and moment bounds for the expectation of order and record statistics based on independent identically distributed random variables. The bounds are attainable providing ...

Let Φ(t) and Ψ(t) be nonnegative convex functions, and let φ and ψ be the right continuous derivatives of Φ and Ψ, respectively. In this paper, we prove the equivalence of the following three conditions: (i) ‖f∗‖Φ ≤ c‖f‖Ψ, (ii) LΨ ⊆ HΦ and (iii) ∫ t s0 φ(s) s ds ≤ cψ(ct), ∀t > s0, where LΨ and HΦ are the Orlicz martingale spaces. As a corollary, we get a sufficient and necessary condition under...

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.

We construct a model of trade with heterogeneous retailers to examine the effects of trade liberalization on retail market structure, imports and social welfare. We are especially interested in studying the degree of pass-through of import into retail prices and the effects of retail market regulation. The paper shows that the degree of pass-through may be large when market structure effects ar...

holds for r > 0 and n∈N. We call the left-hand side of this inequality Alzer’s inequality [1] and the right-hand side Martins’ inequality [8]. Let {ai}i∈N be a positive sequence. If ai+1ai−1 ≥ ai for i ≥ 2, we call {ai}i∈N a logarithmically convex sequence; if ai+1ai−1 ≤ ai for i≥ 2, we call {ai}i∈N a logarithmically concave sequence. In [2], Martins’ inequality was generalized as follows: let ...

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.

We give a new Hilbert-type integral inequality with the best constant factor by estimating the weight function. And the equivalent form is considered.