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A Best Possible Double Inequality for Power Mean
Journal of Applied Mathematics, 2012 We answer the question: for any p,q∈ℝ with p≠q and p≠-q, what are the greatest value λ=λ(p,q) and the least value μ=μ(p,q), such that the double inequality Mλ(a,b)
Yong-Min Li, Bo-Yong Long, Yu-Ming Chu
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Fractional Ostrowski-type Inequalities via $(\alpha,\beta,\gamma,\delta)-$convex Function [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, we are introducing for the first time a generalized class named the class of $(\alpha,\beta,\gamma,\delta)-$convex functions of mixed kind.
Ali Hassan +3 more
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Optimal Inequalities for Power Means [PDF]
Journal of Applied Mathematics, 2012 We present the best possible power mean bounds for the product for any p > 0, α ∈ (0,1), and all a, b > 0 with a ≠ b. Here, Mp(a, b) is the pth power mean of two positive numbers a and b.
Li, Yong-Min +3 more
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Properties of the power-mean and their applications
AIMS Mathematics, 2020 Suppose $w,v>0$, $w\neq v$ and $A_{u}\left (w,v\right) $ is the $u$-order power mean (PM) of $w$ and $v$. In this paper, we completely describe the convexity of $u\mapsto A_{u}\left (w,v\right) $ on $\mathbb{R}$ and $% s\mapsto A_{u\left (s\right ...
Jing-Feng Tian +2 more
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An inequality for mixed power means [PDF]
Mathematical Inequalities & Applications, 1999 This paper contains a weighted version of a mixed power means inequality proved by \textit{B. Mond} and the reviewer [Austral. Math. Soc. Gaz. 23, No. 2, 67-70 (1996; Zbl 0866.26015)]. If \(s>r\) and if \(w= (w_1,w_2,\dots, w_n)\) satisfy \[ W_n w_k- W_k w_n>0\quad\text{for }2\leq k\leq n-1,\tag{\(*\)} \] where \(W_k:= \sum^k_{i=1} w_i\), then \[ m_{r ...
Tarnavas, Christos D. +1 more
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Generalized power means and interpolating inequalities [PDF]
Proceedings of the American Mathematical Society, 1999 Let \(Q_n\subset\mathbb{R}_+^n\) (\(n\geq 2\)) be a non-empty set and \(\mathbf{f}=(f_1,f_2,\dots,f_m)\), where \(f_i:Q_n\rightarrow\mathbb{R}_+\), \(1\leq i\leq m\), are distinct functions. Let also \(w_i>0\), \(1\leq i\leq m\), and \(\Delta(\mathbf{w})=\Delta (w_1, \dots,w_m)\) be the \((m-1)\)-simplex in \(\mathbb{R}^m\) with vertices \((0,\dots,0,1/
Ku, Hsu-Tung +2 more
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Optimal sublinear inequalities involving geometric and power means [PDF]
Mathematica Bohemica, 2009 Summary: There are many relations involving the geometric means \(G_{n}(x)\) and power means \([A_{n}(x^{\gamma })]^{1/\gamma }\) for positive \(n\)-vectors \(x\). Some of them assume the form of inequalities involving parameters. There then is the question of sharpness, which is quite difficult in general.
Wen, Jiajin +2 more
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Maximizing sum rate and minimizing MSE on multiuser downlink: Optimality, fast algorithms and equivalence via max-min SIR [PDF]
, 2009 Maximizing the minimum weighted SIR, minimizing the weighted sum MSE and maximizing the weighted sum rate in a multiuser downlink system are three important performance objectives in joint transceiver and power optimization, where all the users have a ...
Chiang, Mung, Srikant, R., Tan, Chee Wei
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Newton–Simpson-type inequalities via majorization
Journal of Inequalities and Applications, 2023 In this article, the main objective is construction of fractional Newton–Simpson-type inequalities with the concept of majorization. We established a new identity on estimates of definite integrals utilizing majorization and this identity will lead us to
Saad Ihsan Butt +3 more
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Properties of distance spaces with power triangle inequalities
Karpatsʹkì Matematičnì Publìkacìï, 2016 Metric spaces provide a framework for analysis and have several very useful properties. Many of these properties follow in part from the triangle inequality.
D. Greenhoe
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