ON SOME SHARP CHERNOFF TYPE INEQUALITIES

ON SOME SHARP CHERNOFF TYPE INEQUALITIES

ON SOME SHARP CHERNOFF TYPE INEQUALITIES

ON SOME SHARP CHERNOFF TYPE INEQUALITIES

ON SOME SHARP CHERNOFF TYPE INEQUALITIES

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doi:10.1007/s10473-025-0215-6

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (2): 540-552.doi: 10.1007/s10473-025-0215-6

Yuqi ZHOU, Chunna ZENG^*

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

收稿日期:2023-11-23 修回日期:2024-05-13 出版日期:2025-03-25 发布日期:2025-05-08

Yuqi ZHOU, Chunna ZENG^*

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

Received:2023-11-23 Revised:2024-05-13 Online:2025-03-25 Published:2025-05-08
Contact: *Chunna ZENG, E-mail: zengchn@163.com
About author:Yuqi ZHOU, E-mail: zhouyuqi202212@163.com
Supported by:
Yuqi Zhou's research was supported by the Postgraduate Scientic Research Innovation Project of Chongqing Normal University (YKC24010). Chunna Zeng's research was supported by the Major Special Project of the National Natural Science Foundation of China (12141101), the Young Top-Talent program of Chongqing (CQYC2021059145), the Technology Research Foundation of Chongqing Educational committee (KJZD-K202200509) and the Natural Science Foundation Project of Chongqing (CSTB2024NSCQ-MSX0937).

摘要： Two sharp Chernoff type inequalities are derived for star bodies in $\mathbb{R}^2$ , one is an extension of the dual Chernoff-Ou-Pan inequality, and the other is the reverse Chernoff type inequality. Furthermore, we establish a generalized dual symmetric mixed Chernoff inequality for two planar star bodies. As a direct consequence, a new proof of the dual symmetric mixed isoperimetric inequality is presented.

关键词: Chernoff type inequality, Fourier series, $k$ -order radial function, reverse Chernoff type inequality

Abstract: Two sharp Chernoff type inequalities are derived for star bodies in $\mathbb{R}^2$ , one is an extension of the dual Chernoff-Ou-Pan inequality, and the other is the reverse Chernoff type inequality. Furthermore, we establish a generalized dual symmetric mixed Chernoff inequality for two planar star bodies. As a direct consequence, a new proof of the dual symmetric mixed isoperimetric inequality is presented.

Key words: Chernoff type inequality, Fourier series, $k$ -order radial function, reverse Chernoff type inequality

中图分类号:

52A22

Yuqi ZHOU, Chunna ZENG. ON SOME SHARP CHERNOFF TYPE INEQUALITIES[J]. 数学物理学报(英文版), 2025, 45(2): 540-552.

Yuqi ZHOU, Chunna ZENG. ON SOME SHARP CHERNOFF TYPE INEQUALITIES[J]. Acta mathematica scientia,Series B, 2025, 45(2): 540-552.

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