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<p>This article deals with the sharp discrete isoperimetric inequalities in analysis and geometry for planar convex polygons. First, the analytic isoperimetric inequalities based on the 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.</p>

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On Some Discrete Bonnesen-style Isoperimetric Inequalities

  • 期刊论文

  • 发表日期：

    2025年5月15日

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  • Chunna Zeng,
  • Xu Dong

摘要

This article deals with the sharp discrete isoperimetric inequalities in analysis and geometry for planar convex polygons. First, the analytic isoperimetric inequalities based on the 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.