Sharp bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parameters [PDF]
Journal of Inequalities and Applications, 2017 In the article, we present the best possible parameters λ = λ ( p ) $\lambda=\lambda (p)$ and μ = μ ( p ) $\mu=\mu(p)$ on the interval [ 0 , 1 / 2 ] $[0, 1/2]$ such that the double inequality G p [ λ a + ( 1 − λ ) b , λ b + ( 1 − λ ) a ] A 1 − p ( a , b )
Wei-Mao Qian, Yu-Ming Chu
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Optimal two-parameter geometric and arithmetic mean bounds for the Sándor–Yang mean
Journal of Inequalities and Applications, 2019 In the article, we provide the sharp bounds for the Sándor–Yang mean in terms of certain families of the two-parameter geometric and arithmetic mean and the one-parameter geometric and harmonic means.
Wei-Mao Qian +3 more
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One mean to rule them all? The arithmetic mean based egg reduction rate can be misleading when estimating anthelminthic drug efficacy in clinical trials. [PDF]
PLoS Negl Trop Dis, 2020 Animal and human helminth infections are highly prevalent around the world, with only few anthelminthic drugs available. The anthelminthic drug performance is expressed by the cure rate and the egg reduction rate.
Moser W +5 more
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On approximating the quasi-arithmetic mean
Journal of Inequalities and Applications, 2019 In this article, we prove that the double inequalities α1[7C(a,b)16+9H(a,b)16]+(1−α1)[3A(a,b)4+G(a,b)4]
Tie-Hong Zhao +3 more
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Sharp bounds for Neuman means in terms of two-parameter contraharmonic and arithmetic mean
Journal of Inequalities and Applications, 2019 In the article, we prove that λ1=1/2+[(2+log(1+2))/2]1/ν−1/2 $\lambda _{1}=1/2+\sqrt{ [ (\sqrt{2}+ \log (1+\sqrt{2}) )/2 ]^{1/\nu }-1}/2$, μ1=1/2+6ν/(12ν) $\mu _{1}=1/2+\sqrt{6 \nu }/(12\nu )$, λ2=1/2+[(π+2)/4]1/ν−1/2 $\lambda _{2}=1/2+\sqrt{ [(\pi +2)/4
Wei-Mao Qian +3 more
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Bounds for Combinations of Toader Mean and Arithmetic Mean in Terms of Centroidal Mean [PDF]
The Scientific World Journal, 2013 The authors find the greatest value λ and the least value μ, such that the double inequality C¯(λa+(1-λb),λb+(1-λ)a)
Wei-Dong Jiang
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Revisiting Fold-Change Calculation: Preference for Median or Geometric Mean over Arithmetic Mean-Based Methods [PDF]
BiomedicinesBackground: Fold change is a common metric in biomedical research for quantifying group differences in omics variables. However, inconsistent calculation methods and inadequate reporting lead to discrepancies in results. This study evaluated various fold-
Jörn Lötsch +2 more
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On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind
Journal of Mathematical Analysis and Applications, 2018 In the article, we prove that the double inequalities 1 + ( 6 p − 7 ) r ′ p + ( 5 p − 6 ) r ′ π tanh − 1 ( r ) 2 r K ( r ) 1 + ( 6 q − 7 ) r ′ q + ( 5 q − 6 ) r ′ π tanh − 1 ( r ) 2 r , q A ( 1 , r ) + ( 5 q − 6 ) G ( 1 , r ) A ( 1 , r ) + ( 6 q − 7 )
Zhen-Hang Yang +2 more
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The invariance of the arithmetic mean with respect to generalized quasi-arithmetic means
Journal of Mathematical Analysis and Applications, 2009 Given a continuous strictly monotone function \(\phi: I\to {\mathbb R}\) and a probability measure \(\mu\) on the Borel subjects of \([0,1],\) the two variable mean \({\mathcal M}_{\phi, \mu}: I^2\to I\) is defined by \[ {\mathcal M}_{\phi, \mu}(x,y)=\phi^{-1}\left(\int_0^1 \phi(tx+(1-t)y)d\mu(t)\right), \quad (x,y)\in I. \] The aim of this paper is to
Zsolt Pales
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Pre-service Teachers’ Common Content Knowledge Regarding the Arithmetic Mean
REDIMAT, 2014 The main goal of this study is to determine the common content knowledge of a group of pre-service primary teachers regarding the arithmetic mean. The cognitive configuration tool proposed by the Onto-semiotic Approach of Cognition and Mathematics ...
Juan Jesús Ortiz de Haro +1 more
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