Chinese Quarterly Journal of Mathematics ›› 2006, Vol. 21 ›› Issue (2): 210-219.

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A Class of the Geometric Inequalities Involving k-Brocard Distance

  

  1. 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)；

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Abstract: Let P be an inner point of a convex N-gon ΓN:A1A2…ANA1(N≥3), and let di,k denote the distance from the point Ai+k, to the line PAi(i=1,2,…,N,Ai=Aji=j(modN)), which is called the k-Brocard distance for P of ΓN. We have proved the following double-inequality: If P∈ΓN, and then ... .

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

CLC Number: 

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