含k-Brocard距离的一类几何不等式

数学季刊 ›› 2006, Vol. 21 ›› Issue (2): 210-219.

含k-Brocard距离的一类几何不等式

Department of Mathematics and Computer Science, Chengdu University, Chengdu 610106 China; Department of Mathematics, Guangzhou Maritime College, Guangzhou 510725, China;College of Mathematics, Sichuan University, Chengdu 610024, China

收稿日期:2004-06-09 出版日期:2006-06-30 发布日期:2023-12-06
作者简介:WEN Jia-jin(1961-),male,native of Anyue,Sichuan,an associate professor of Chengdu Univer- sity,M.S.D.,engages in inequality theory.
基金资助:
Supported by the NSF of China(10171073)；

A Class of the Geometric Inequalities Involving k-Brocard Distance

Department of Mathematics and Computer Science, Chengdu University, Chengdu 610106 China; Department of Mathematics, Guangzhou Maritime College, Guangzhou 510725, China;College of Mathematics, Sichuan University, Chengdu 610024, China

Received:2004-06-09 Online:2006-06-30 Published:2023-12-06
About author:WEN Jia-jin(1961-),male,native of Anyue,Sichuan,an associate professor of Chengdu Univer- sity,M.S.D.,engages in inequality theory.
Supported by:
Supported by the NSF of China(10171073)；

摘要/Abstract

摘要： Let P be an inner point of a convex N-gon Γ_N:A₁A₂…A_NA₁(N≥3), and let di,k denote the distance from the point A_i+k, to the line PA_i(i=1,2,…,N,A_i=A_ji=j(modN)), which is called the k-Brocard distance for P of Γ_N. We have proved the following double-inequality: If P∈Γ_N, and then ... .

关键词: convex , N-gon;k-Brocard , distance;Holder , inequality;Janous-Klamkin's , con-
jecture

Abstract: Let P be an inner point of a convex N-gon Γ_N:A₁A₂…A_NA₁(N≥3), and let di,k denote the distance from the point A_i+k, to the line PA_i(i=1,2,…,N,A_i=A_ji=j(modN)), which is called the k-Brocard distance for P of Γ_N. We have proved the following double-inequality: If P∈Γ_N, and then ... .

Key words: convex , N-gon;k-Brocard , distance;Holder , inequality;Janous-Klamkin's , con-
jecture

中图分类号:

O157.3

文家金, 柯睿, 吕涛. 含k-Brocard距离的一类几何不等式[J]. 数学季刊, 2006, 21(2): 210-219.

WEN Jia-jin, KE Rui, LV Tao. A Class of the Geometric Inequalities Involving k-Brocard Distance[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(2): 210-219.