The best possible Lehmer mean bounds for a convex combination of logarithmic and harmonic means
نویسندگان
چکیده
منابع مشابه
Optimal convex combinations bounds of centrodial and harmonic means for logarithmic and identric means
We find the greatest values $alpha_{1} $ and $alpha_{2} $, and the least values $beta_{1} $ and $beta_{2} $ such that the inequalities $alpha_{1} C(a,b)+(1-alpha_{1} )H(a,b)
متن کاملoptimal convex combinations bounds of centrodial and harmonic means for logarithmic and identric means
we find the greatest values $alpha_{1} $ and $alpha_{2} $, and the least values $beta_{1} $ and $beta_{2} $ such that the inequalities $alpha_{1} c(a,b)+(1-alpha_{1} )h(a,b)
متن کاملOptimal Bounds for Neuman–sándor Mean in Terms of the Convex Combination of Logarithmic and Quadratic or Contra–harmonic Means
In this article, we present the least values α1 , α2 , and the greatest values β1 , β2 such that the double inequalities α1L(a,b)+(1−α1)Q(a,b) < M(a,b) < β1L(a,b)+(1−β1)Q(a,b) α2L(a,b)+(1−α2)C(a,b) < M(a,b) < β2L(a,b)+(1−β2)C(a,b) hold for all a,b > 0 with a = b , where L(a,b) , M(a,b) , Q(a,b) and C(a,b) are respectively the logarithmic, Neuman-Sándor, quadratic and contra-harmonic means of a ...
متن کاملOptimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means
and Applied Analysis 3 Alzer and Qiu 27 found the sharp bound of 1/2 L a, b I a, b in terms of the power mean as follows: Mc a, b < 1 2 L a, b I a, b 1.8 for all a, b > 0 with a/ b, with the best possible parameter c log 2/ 1 log 2 . The main purpose of this paper is to find the least value λ ∈ 0, 1 and the greatest value p p α such that αH a, b 1 − α L a, b > Mp a, b for α ∈ λ, 1 and all a, b ...
متن کاملOptimal One–parameter Mean Bounds for the Convex Combination of Arithmetic and Logarithmic Means
We find the greatest value p1 = p1(α) and the least value p2 = p2(α) such that the double inequality Jp1 (a,b) <αA(a,b)+(1−α)L(a,b) < Jp2 (a,b) holds for any α ∈ (0,1) and all a,b > 0 with a = b . Here, A(a,b) , L(a,b) and Jp(a,b) denote the arithmetic, logarithmic and p -th one-parameter means of two positive numbers a and b , respectively. Mathematics subject classification (2010): 26E60.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematical Forum
سال: 2013
ISSN: 1314-7536
DOI: 10.12988/imf.2013.37135