Some inequalities for the (p,q)-mixed geominimal surface areas and Lp radial Blaschke-Minkowski homomorphisms

Wang et al. introduced Lp radial Blaschke-Minkowski homomorphisms based on Schuster?s radial Blaschke-Minkowski homomorphisms. In 2018, Feng and He gave the concept of (p,q)-mixed geominimal surface area according to the Lutwak, Yang and Zhang?s (p,q)-mixed volume. In this article, associated with the (p,q)-mixed geominimal surface areas and the Lp radial Blaschke-Minkowski homomorphisms, we establish some inequalities including two Brunn-Minkowski type inequalities, a cyclic inequality and two monotonic inequalities.

The Cyclic Inequality of N.P. Korneichuk and it’s generalization

In this paper there is given a generalization of well-known cyclic inequality of N.P. Korneichuk on the case of n independent variables. This result is of independent interest and can be used to obtain estimated results of splines-approximation in classes with bounded modulus of continuity.

Dual mixed complex brightness integrals

In this paper, we define the dual mixed complex brightness integrals and establish related Brunn-Minkowski type inequality, Aleksandrov-Fenchel inequality, cyclic inequality and monotonicity inequality, respectively. As applications, we give the analogous version of the differences inequalities for the dual mixed complex brightness integrals

Cyclic Inequality Forms with Power 1/2,1/3

The purpose of this paper is to establish inequalities between two terms \begin{equation*} F =\sum_{i=1}^{n}\sqrt{ax_{i}^{2}+bx_{i}x_{i+1}+cx_{i+1}^{2}+dx_i+ex_{i+1}+d }; \end{equation*} \begin{equation*} G =\sum_{i=1}^{n}\sqrt[3]{ax_{i}^{3}+bx_{i}^{2}x_{i+1}+cx_{i}x_{i+1}^{2}+dx_{i+1}^{3}}, \end{equation*} and $\sum_{i=1}^{n}x_{i}$ for a sequence of cyclic positive real numbers $ (x_{i})_{i=1}^{n+1}$ with $x_{n+1}=x_{1}$. The results depends on the sign of expressions containing the coefficients $a,b,c,d$. The general case for $F$ is also investigated.

ISOPERIMETRIC INEQUALITIES FOR Lp GEOMINIMAL SURFACE AREA

In this paper, we establish a number of Lp-affine isoperimetric inequalities for Lp-geominimal surface area. In particular, we obtain a Blaschke–Santaló type inequality and a cyclic inequality between different Lp-geominimal surface areas of a convex body.