- Turkish Journal of Mathematics
- Vol: 40 Issue: 2
- The dual generalized Chernoff inequality for star-shaped curves
The dual generalized Chernoff inequality for star-shaped curves
Authors : Deyan Zhang, Yunlong Yang
Pages : 272-282
View : 6 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :In this paper, we first introduce the $k$-order radial function $\rho_k(\theta)$ for star-shaped curves in $\mathbb{R}^2$ and then prove a geometric inequality involving $\rho_k(\theta)$ and the area $A$ enclosed by a star-shaped curve, which can be looked upon as the dual Chernoff--Ou--Pan inequality. As a by-product, we get a new proof of the classical dual isoperimetric inequality. We also prove that $\frac{C^2}{k^2}\leq AKeywords : Star curves, the dual Chernoff--Ou--Pan inequality, equichordal curves