Turkish Journal of Mathematics
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
DOI
10.3906/mat-1504-12
Keywords
Star curves, the dual Chernoff--Ou--Pan inequality, equichordal curves
First Page
272
Last Page
282
Recommended Citation
ZHANG, D, & YANG, Y (2016). The dual generalized Chernoff inequality for star-shaped curves. Turkish Journal of Mathematics 40 (2): 272-282. https://doi.org/10.3906/mat-1504-12
