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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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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Optimal inequalities for bounding Toader mean by arithmetic and quadratic means [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we present the best possible parameters α ( r ) $\alpha(r)$ and β ( r ) $\beta(r)$ such that the double inequality [ α ( r ) A r ( a , b ) + ( 1 − α ( r ) ) Q r ( a , b ) ] 1 / r < T D [ A ( a , b ) , Q ( a , b ) ] < [ β ( r ) A r ( a , b )
Tie-Hong Zhao, Yu-Ming Chu, Wen Zhang
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Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we find the greatest values α 1 , α 2 $\alpha_{1},\alpha_{2}$ and the smallest values β 1 , β 2 $\beta_{1},\beta_{2}$ such that the double inequalities L α 1 ( a , b ) < AG ( a , b ) < L β 1 ( a , b ) $L_{\alpha_{1}}(a,b)0$ with a ≠ b $a ...
Qing Ding, Tiehong Zhao
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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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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 Páles
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Factors for Absolute Weighted Arithmetic Mean Summability of Infinite Series
International Journal of Analysis and Applications, 2017 In this paper, we proved a general theorem dealing with absolute weighted arithmetic mean summability factors of infinite series under weaker conditions. We have also obtained some known results.
Hüseyin Bor
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Bounds for the Neuman–Sándor Mean in Terms of the Arithmetic and Contra-Harmonic Means [PDF]
Axioms, 2022 Wen-Hui Li, Peng Miao, Bai-Ni Guo
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Stochastic Order and Generalized Weighted Mean Invariance
Entropy, 2021 In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines ...
Mateu Sbert +3 more
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