Bounds for the Combinations of Neuman-Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean [PDF]
Abstract and Applied Analysis, 2013 We give the greatest values r1, r2 and the least values s1, s2 in (1/2, 1) such that the double inequalities C(r1a+(1-r1)b,r1b+(1-r1)a)
Zai-Yin He +4 more
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A Nice Separation of Some Seiffert-Type Means by Power Means [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 Seiffert has defined two well-known trigonometric means denoted by 𝒫 and 𝒯. In a similar way it was defined by Carlson the logarithmic mean ℒ as a hyperbolic mean. Neuman and Sándor completed the list of such means by another hyperbolic mean ℳ. There are
Iulia Costin, Gheorghe Toader
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Best Possible Bounds for Neuman-Sándor Mean by the Identric, Quadratic and Contraharmonic Means
Abstract and Applied Analysis, 2013 We prove that the double inequalities Iα1(a,b)Q1-α1(a,b)
Tie-Hong Zhao +3 more
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Optimal bounds for two Sándor-type means in terms of power means [PDF]
Journal of Inequalities and Applications, 2016 In the article, we prove that the double inequalities M α ( a , b ) < S Q A ( a , b ) < M β ( a , b ) $M_{\alpha }(a,b)< S_{QA}(a,b)< M_{\beta}(a,b)$ and M λ ( a , b ) < S A Q ( a , b ) < M μ ( a , b ) $M_{\lambda }(a,b)< S_{AQ}(a,b)< M_{\mu}(a,b)$ hold ...
Tie-Hong Zhao +2 more
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Index of a bivariate mean and applications
Journal of Inequalities and Applications, 2016 Exploring some results of (Raïssouli in J. Math. Inequal. 10(1):83-99, 2016) from another point of view, we introduce here some power-operations for (bivariate) means.
Mustapha Raïssouli
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Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means
Journal of Applied Mathematics, 2013 We present the largest values α1, α2, and α3 and the smallest values β1, β2, and β3 such that the double inequalities α1M(a,b)+(1-α1)H(a,b)
Fan Zhang, Yu-Ming Chu, Wei-Mao Qian
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A separation of some Seiffert-type means by power means [PDF]
Journal of Numerical Analysis and Approximation Theory, 2012 Consider the identric mean \(\mathcal{I}\), the logarithmic mean \(\mathcal{L,}\) two trigonometric means defined by H. J. Seiffert and denoted by \(\mathcal{P}\) and \(\mathcal{T,}\) and the hyperbolic mean \(\mathcal{M}\) defined by E.
Iulia Costin, Gheorghe Toader
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A unified proof of several inequalities and some new inequalities involving Neuman-S\'andor mean [PDF]
, 2014 In the paper, by finding linear relations of differences between some means, the authors supply a unified proof of some double inequalities for bounding Neuman-Sandor means in terms of the arithmetic, harmonic, and contra-harmonic means and discover some
Feng Qi (祁锋), Wen-Hui Li
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Sharp bounds for the Neuman-Sándor mean in terms of the power and contraharmonic means [PDF]
, 2015 In the paper, the authors obtain sharp bounds in terms of the power of the contra-harmonic mean for Neuman-Sándor mean.
Weidong Jiang, Feng Qi (祁锋)
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Sharpness of Wilker and Huygens type inequalities [PDF]
, 2012 We present an elementary proof of Wilker's inequality involving trigonometric functions, and establish sharp Wilker and Huygens type inequalities.
Chen, CP, Cheung, WS
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