The Weighted Arithmetic Mean–Geometric Mean Inequality is Equivalent to the Hölder Inequality [PDF]
Symmetry, 2018 In the current note, we investigate the mathematical relations among the weighted arithmetic mean–geometric mean (AM–GM) inequality, the Hölder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical equivalence among the weighted AM–GM inequality, the weighted power-mean inequality and the Hölder inequality are fully ...
Yongtao Li, Xian-Ming Gu, Jianxing Zhao
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Refining and reversing the weighted arithmetic–geometric mean inequality involving convex functionals and application for the functional entropy [PDF]
Journal of Inequalities and Applications, 2020 In this paper, we present some refinements and reverses for some inequalities involving the weighted arithmetic mean and the weighted geometric mean of two convex functionals. Inequalities involving the Heinz functional mean are also obtained.
Mustapha Raïssouli, Mashael Almozini
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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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Weighted Versions of the Arithmetic-Mean-Geometric Mean Inequality and Zaremba's Function [PDF]
, 2023 We use the weighted version of the arithmetic-mean-geometric-mean inequality to motivate new results about Zaremba's function, $z(n) = \sum_{d|n} \frac{\log d}{d}$. We investigate record-setting values for $z(n)$ and the related function $v(n) = \frac{z(n)}{\log τ(n)}$ where $τ(n)$ is the number of divisors of $n$.
McCormack, Tim, Zelinsky, Joshua
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On Gauss compounding of symmetric weighted arithmetic means
Journal of Mathematical Analysis and Applications, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abu-Saris, Raghib, Hajja, Mowaffaq
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Schur convexity properties of the weighted arithmetic integral mean and Chebyshev functional
Journal of Numerical Analysis and Approximation Theory, 2013 In this paper, we discuss the Schur convexity, Schur geometrical convexity and Schur harmonic convexity of the weighted arithmetic integral mean and Chebyshev functional.
Long Bo-Yong +2 more
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The matrix geometric mean of parameterized, weighted arithmetic and harmonic means
Linear Algebra and its Applications, 2011 For positive definite matrices \(C\) and \(D\), the matrix geometric mean \(C \sharp D\) is the metric midpoint of the of arithmetic mean \(A = \frac12(C + D)\) and the harmonic mean \(H = 2(C^{-1} + D^{-1})^{-1}\) for the trace metric. The authors consider the more general construction of taking the geometric mean of the weighted \(n\)-variable ...
Kim, Sejong, Lawson, Jimmie, Lim, Yongdo
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A Newton-Modified Weighted Arithmetic Mean Solution of Nonlinear Porous Medium Type Equations [PDF]
Symmetry, 2021 Elayaraja Aruchunan +4 more
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On consistency of the weighted arithmetical mean complex judgement matrix
Journal of Systems Engineering and Electronics, 2007 The weighted arithmetical mean complex judgement matrix (WAMCJM) is the most common method for aggregating group opinions, but it has a shortcoming, namely the WAMCJM of the perfectly consistent judgement matrices given by experts canot guarantee its perfect consistency. An upper bound of the WAMCJM's consistency is presented.
Dong Yucheng, Xu Yinfeng, Ding Lili
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On the generalized weighted quasi-arithmetic integral mean
International Journal of Mathematical Analysis, 2013 Hui Sun, Boyong Long, Yuming Chu
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