Abstract
In this paper, we derive an improved sharp version of a reverse isoperimetric inequality for convex planar curves of Pan and Zhang (Beitrage Algebra Geom 48:303–308, 2007), with a simpler Fourier series proof. Moreover our result also confirm a conjecture by Pan et al. (J Math Inequal (preprint), 2010). Furthermore we also present a stability property of our reverse isoperimetric inequality (near equality implies curve nearly circular).
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