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Optimal bounds for two Seiffert–like means in exponential type

Journal of Mathematical Analysis and Applications, 2022
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Ling Zhu
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Optimal evaluations of some Seiffert-type means by power means

Applied Mathematics and Computation, 2013
Let us consider the second trigonometric mean T defined by Seiffert and the hyperbolic mean M defined by Neuman and Sandor. There are some known inequalities between these means and some power means A"p. We prove that the evaluationsA"l"n"2"/"l"n"("l"n"("3"+"2"2")")
Iulia Costin, Gheorghe Toader
exaly   +2 more sources

Optimal bounds for two Seiffert-like means by arithmetic mean and harmonic mean

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2023
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Ling Zhu, Branko Malesevic
exaly   +3 more sources

Sharp generalized Seiffert mean bounds for the Toader mean of order 4

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2021
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Yanlin Li, Tie-Hong Zhao
exaly   +3 more sources

Sharp bounds for Seiffert mean in terms of root mean square [PDF]

Journal of Inequalities and Applications, 2012
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Yu-Ming Chu
exaly   +2 more sources

Optimal bounds of exponential type for arithmetic mean by Seiffert-like mean and centroidal mean

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ling Zhu
exaly   +3 more sources

The optimal generalized logarithmic mean bounds for Seiffert's mean

Acta Mathematica Scientia, 2012
Abstract For p ∈ R , the generalized logarithmic mean L p ( a,b ) and Seiffert's mean T ( a,b ) of two positive real numbers a and b are defined in (1.1) and (1.2) below respectively. In this paper, we find the greatest p and least q such that the double-inequality L p ( a,b ) T ( a,b ) L q ( a,b ) holds for all a,b > 0 and a ...
Chu Yuming, Wang Miaokun, Wang Gendi
exaly   +2 more sources

Sharp bounds for the Neuman mean in terms of the quadratic and second Seiffert means [PDF]

Journal of Inequalities and Applications, 2014
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Yu-Ming Chu, Tie-Hong Zhao
exaly   +3 more sources

Bounds for Toader Mean in Terms of Arithmetic and Second Seiffert Means

Communications in Mathematics and Applications, 2019
In the article, we prove that the double inequalities \begin{align*} &\alpha_{1}T(a,b)+(1-\alpha_{1})A(a,b) 0\) with \(a\neq b\) if and only if \(\alpha_{1}\leq 3/4\), \(\beta_{1}\geq1\), \(\alpha_{2}\leq 3/4\) and \(\beta_{2}\geq 1\), where \(A(a,b)\), \(TD(a,b)\) and \(T(a,b)\) are the arithmetic, Toader and second Seiffert means of \(a\) and \(b ...
Zai-Yin He, Yue-Ping Jiang, Yu-Ming Chu
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Sharp weighted Hölder mean bounds for Seiffert's means

Mathematical Inequalities & Applications
Summary: Let \(P(a,b)\) and \(T(a,b)\) be the first and second Seiffert's means for two positive numbers \(a\)and \(b\), in this paper, for any fixed \(p \in \mathbb{R}\), we present the optimal parameters \(\alpha_p\), \(\beta_p\), \(\lambda_p\), \(\mu_p \in [0,1]\) \[ H_p (a,b; \alpha_p) \leqslant P(a,b) \leqslant H_p (a,b; \beta_p),\quad H_p (a,b ...
Zhao, Tie-Hong, Wang, Miao-Kun
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