用反调和均值表示Toader均值和算术均值组合的二重不等式

Publications De L'institut Mathematique Pub Date : 2014-02-19 DOI:10.2298/PIM141026009J

Weidong Jiang, Feng Qi (祁锋)

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引用次数: 7

摘要

对于所有α(0,1)和a,b > 0且a≠b的情况下，λ的最大值和μ的最小值使得二重不等式C(λa +(1-λ)b， λb +(1-λ) a) < α a (a,b) +(1 -α)T(a, b)< C(μa +(1 -μ)b， μb +(1 -μ)a)成立，其中C(a,b)， a (a,b)和T(a,b)分别表示两个正数a和b的反调和、算术和Toader均值。

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A double inequality for the combination of Toader mean and the arithmetic mean in terms of the contraharmonic mean

We find the greatest value λ and the least value μ such that the double inequality C(λa +(1-λ)b, λb + (1-λ)a) < αA(a,b) + (1-α)T(a, b)< C(μa + (1-μ)b, μb + (1-μ)a) holds for all α  (0,1) and a, b > 0 with a ≠ b, where C(a,b), A(a,b), and T(a,b) denote respectively the contraharmonic, arithmetic, and Toader means of two positive numbers a and b.

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Publications De L'institut Mathematique

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