on some discrete Bonnesen-style isoperimetric inequalities

TL;DR

This paper establishes sharp discrete isoperimetric inequalities for planar convex polygons, including analytic, Bonnesen-style, and inverse Bonnesen-style inequalities, advancing geometric analysis in discrete settings.

Contribution

It introduces new sharp discrete isoperimetric inequalities for convex polygons, extending classical results with Bonnesen-style inequalities and their inverses.

Findings

Established analytic isoperimetric inequalities based on Schur convex functions.

Derived Bonnesen-style inequalities for planar convex polygons.

Obtained inverse Bonnesen-style inequalities for convex polygons.

Abstract

This article deals with the sharp discrete isoperimetric inequalities in analysis and geometry for planar convex polygons. First, the analytic isoperimetric inequalities based on Schur convex function are established. In the wake of the analytic isoperimetric inequalities, Bonnesen-style isoperimetric inequalities and inverse Bonnesen-style inequalities for the planar convex polygons are obtained.