We present symmetric Rogers--Hölder's inequalities on time scales when $frac{1}{p}+frac{1}{q}+frac{1}{r}=0$ and $frac{r}{p}+frac{r}{q}$ is not necessarily equal to $1$ where $p,$ $q$ and $r$ are nonzero real numbers.

In this paper our aim is to deduce some complete monotonicity properties and functional inequalities for the Bickley function. The key tools in our proofs are the classical integral inequalities, like Chebyshev, Hölder-Rogers, Cauchy-Schwarz, Carlson and Grüss inequalities, as well as the monotone form of l’Hospital’s rule. Moreover, we prove the complete monotonicity of a determinant function ...

In this paper, inequalities for quermassintegrals and dual quermassintegrals of difference bodies are given. In particular, an extension of the Rogers-Shephard inequality is obtained. Mathematics subject classification (2010): 52A40, 52A20.

A criterion is established for the validity of multilinear inequalities of a class considered by Brascamp and Lieb, generalizing well-known inequalties of Rogers and Hölder, Young, and Loomis-Whitney. 1. Formulation Consider multilinear functionals (1.1) Λ(f1, f2, · · · , fm) = ∫