摘要
In this article, we prove that the symmetric function Fn(x,r)=∑i1+i2+……in=r(x1(i1x2^i2……xn^in)1/r is Schur harmonic convex for x ∈ R+n and r ∈N -=(1, 2, 3,...} As its applications, some analytic inequalities are established.
In this article, we prove that the symmetric function Fn(x,r)=∑i1+i2+……in=r(x1(i1x2^i2……xn^in)1/r is Schur harmonic convex for x ∈ R+n and r ∈N -=(1, 2, 3,...} As its applications, some analytic inequalities are established.
基金
supported by NSFC (60850005)
NSF of Zhejiang Province(D7080080, Y7080185, Y607128)