数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1501-1506.doi: 10.1016/S0252-9602(10)60142-7

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THE SCHUR HARMONIC CONVEXITY FOR A CLASS OF SYMMETRIC FUNCTIONS

褚玉明, 孙天川   

  1. Department of Mathematics, Huzhou Teachers College, Huzhou 313000, |China
  • 收稿日期:2008-08-23 出版日期:2010-09-20 发布日期:2010-09-20
  • 基金资助:

    This work was supported by NSFC (60850005) and NSF of Zhejiang Province (D7080080, Y7080185, Y607128).

THE SCHUR HARMONIC CONVEXITY FOR A CLASS OF SYMMETRIC FUNCTIONS

 CHU Yu-Ming, SUN Tian-Chuan   

  1. Department of Mathematics, Huzhou Teachers College, Huzhou 313000, |China
  • Received:2008-08-23 Online:2010-09-20 Published:2010-09-20
  • Supported by:

    This work was supported by NSFC (60850005) and NSF of Zhejiang Province (D7080080, Y7080185, Y607128).

摘要:

In this article, we prove that the symmetric function
 Fn*(x, r)=∑i1+i2+…+in=r(x1i1x2i2xnin )1/r is Schur harmonic convex for x ∈R+n and r ∈ N={1, 2, 3, …}. As its applications, some analytic inequalities are established.

关键词: symmetric function, Schur convex, Schur harmonic convex

Abstract:

In this article, we prove that the symmetric function
 Fn*(x, r)=∑i1+i2+…+in=r(x1i1x2i2xnin )1/r is Schur harmonic convex for x ∈R+n and r ∈ N={1, 2, 3, …}. As its applications, some analytic inequalities are established.

Key words: symmetric function, Schur convex, Schur harmonic convex

中图分类号: 

  • 26B25