Turkish Journal of Mathematics
DOI
10.3906/mat-1504-12
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 A
Keywords
Star curves, the dual Chernoff--Ou--Pan inequality, equichordal curves
First Page
272
Last Page
282
Recommended Citation
ZHANG, DEYAN and YANG, YUNLONG
(2016)
"The dual generalized Chernoff inequality for star-shaped curves,"
Turkish Journal of Mathematics: Vol. 40:
No.
2, Article 4.
https://doi.org/10.3906/mat-1504-12
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss2/4
