Results 221 to 230 of about 1,289,599 (266)

Two-Variable Wasserstein Means of Positive Definite Operators

Mediterranean Journal of Mathematics, 2022
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Hwang, Jinmi, Kim, Sejong
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Inequalities for Means in Two Variables

Archiv der Mathematik, 2003
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Alzer, Horst, Qiu, Song-liang
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On two-variable means with variable weights

Aequationes mathematicae, 2004
The two-variable equality problem of two weighted quasi-arithmetic means was solved by \textit{L. Losonczi} [Aequationes Math. 58, 223--241 (1999; Zbl 0939.39015)] under the supposition of six times differentiability of the functions involved. The authors first prove a regularity theorem saying that every solution of a Pexider type functional equation ...
Daróczy, Zoltán, Maksa, Gyula, Páles, Zsolt   +2 more
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On a class of means of two variables

Publicationes Mathematicae Debrecen, 1999
Let \(L\) be a mean value (continuous, symmetric, between max and min) on an open real interval \(I\). The author defines \[ L_{\varphi}(x,y)=\varphi^{-1}(\varphi(x)+\varphi(y)-\varphi[L(x,y)]), \] where \(\varphi\) is a continuous real valued function on \(I\).
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A Multivariable Extension of Two-Variable Matrix Means

SIAM Journal on Matrix Analysis and Applications, 2011
In this article a method for extending two-variable matrix means to several variables is provided as a limit point, based on directly the two-variable forms of matrix means. The convergence of this extension method, hence its applicability, is proved in full generality for any two-variable matrix mean.
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Inequalities for differences of power means in two variables

Analysis Mathematica, 2011
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Wu, Shanhe, Debnath, Lokenath
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Equality of two variable means revisited

Aequationes mathematicae, 2006
Let I be an interval, $$ f,g:I \to \mathbb{R} $$ be given continuous functions such that g(x)≠ 0 for x ∈I and h(x) : = f(x)/g(x) (x ∈I) is strictly monotonic (thus invertible) on I. Let further μ be an increasing non-constant function on [0, 1].
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Homogeneous symmetric means of two variables

Aequationes mathematicae, 2007
Let \(f, g: I \rightarrow{\mathbb{R}}\) be given continuous functions on the interval I such that g ≠ 0, and \(h :=\frac{f}{g}\) is strictly monotonic (thus invertible) on I. Taking an increasing nonconstant function μ on [0, 1] $$ M_{f,g,\mu}(x, y) := h^{-1}\left(\frac{\int \limits_0^1f(tx + (1-t)y)\,d\mu(t)}{\int \limits_0^1g(tx + (1- t)y)\,d\mu ...
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Equality of two variable Cauchy mean values

aequationes mathematicae, 2003
Given two differentiable real functions \(f,g:I\to \mathbb{R}\) such that \(g'\neq 0\) and \(f'/g'\) is invertible on \(I\), the two variable Cauchy mean \(D_{f,g}\) of two elements \(x\neq y\) of the interval \(I\) is defined as \[ D_{f,g}(x,y):=\left({f'\over g'}\right)^{-1} \left({f(x)-f(y)\over g(x)-g(y)}\right).
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