Results 21 to 30 of about 902,467 (342)

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 ...
Christos D. Tarnavas, Dimitrios D. Tarnavas   +1 more
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The optimization for the inequalities of power means [PDF]

Journal of Inequalities and Applications, 2006
Let be the th power mean of a sequence of positive real numbers, where , and . In this paper, we will state the important background and meaning of the inequality ; a necessary and sufficient condition and another interesting sufficient condition that the foregoing inequality holds are obtained; an open problem posed by Wang et al. in 2004 is solved
Wan-Lan Wang, Jiajin Wen
openaire   +3 more sources

Some Inequalities for Power Means; a Problem from “The Logarithmic Mean Revisited”

The American Mathematical Monthly, 2023
G. J. O. Jameson
openalex   +2 more sources

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/
Mei-Chin Ku, Hsu-Tung Ku, Xin-Min Zhang
openaire   +2 more sources

Weak log-majorization and inequalities of power means

The Electronic Journal of Linear Algebra, 2023
As noncommutative versions of the quasi-arithmetic mean, we consider the Lim-Pálfia's power mean, Rényi right mean, and Rényi power means. We prove that the Lim-Pálfia's power mean of order $t \in [-1,0)$ is weakly log-majorized by the log-Euclidean mean and fulfills the Ando-Hiai inequality.
Miran Jeong, Sejong Kim
openaire   +2 more sources

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
core   +1 more source

Optimal power mean bounds for the second Yang mean

Journal of Inequalities and Applications, 2016
In this paper, we present the best possible parameters p and q such that the double inequality Mp(a,b)0$ with a≠b$a\neq b$, where Mr(a,b)=[(ar+br)/2]1/r$M_{r}(a,b)=[(a^{r}+b^{r})/2]^{1/r}$ (r≠0$r\neq0$) and M0(a,b)=ab$M_{0}(a,b)= \sqrt {ab}$ is the rth ...
Jun-Feng Li, Zhen-Hang Yang, Y. Chu
semanticscholar   +2 more sources

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
doaj   +1 more source

Fractional Ostrowski Type Inequalities via $\phi-\lambda-$Convex Function [PDF]

Sahand Communications in Mathematical Analysis
In this paper, we aim to  state well-known Ostrowski inequality via fractional Montgomery identity for the class of $\phi-\lambda-$ convex functions. This generalized class of convex function contains other well-known convex functions from literature ...
Ali Hassan, Asif Khan
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The Rigorous Derivation of the 2D Cubic Focusing NLS from Quantum Many-body Evolution [PDF]

, 2015
We consider a 2D time-dependent quantum system of $N$-bosons with harmonic external confining and \emph{attractive} interparticle interaction in the Gross-Pitaevskii scaling.
Chen, Xuwen, Holmer, Justin
core   +1 more source