Results 31 to 40 of about 77,460 (224)
, 2023 We generalize quasi-arithmetic means beyond scalars by considering the gradient map of a Legendre type real-valued function. The gradient map of a Legendre type function is proven strictly comonotone with a global inverse. It thus yields a generalization of strictly mononotone and differentiable functions generating scalar quasi-arithmetic means ...
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Quasi-arithmetic means of continuous functions
Journal of the Mathematical Society of Japan, 1986 Let I be a proper interval, X a compact Hausdorff space and C(X,I) the set of continuous mappings from X into I. The authors define a mean on C(X,I) as a continuous functional satisfying \(M(a1_ X)=a\) for all \(a\in I\) and Mf\(\leq Mg\) if \(f\leq g\).
ITO, Takashi, NARA, Chie
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Subcommutativity of integrals and quasi-arithmetic means
, 2023 Let $(X, \mathscr{L}, λ)$ and $(Y, \mathscr{M}, μ)$ be finite measure spaces for which there exist $A \in \mathscr{L}$ and $B \in \mathscr{M}$ with either $0 < λ(A) < 1 < λ(X)$ and $0 < μ(B) < μ(Y)$, or the other way around. In addition, let $I \subseteq \mathbb{R}$ be a non-empty open interval, and suppose that $f,g\colon I \to \mathbb ...
Glazowska, Dorota +3 more
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On a functional equation related to two-variable weighted quasi-arithmetic means [PDF]
, 2017 In this paper, we are going to describe the solutions of the functional equation $$ \varphi\Big(\frac{x+y}{2}\Big)(f(x)+f(y))=\varphi(x)f(x)+\varphi(y)f(y) $$ concerning the unknown functions $\varphi$ and $f$ defined on an open interval.
Kiss, Tibor, Páles, Zsolt
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On the Jensen–Shannon Symmetrization of Distances Relying on Abstract Means
Entropy, 2019 The Jensen–Shannon divergence is a renowned bounded symmetrization of the unbounded Kullback–Leibler divergence which measures the total Kullback–Leibler divergence to the average mixture distribution.
Frank Nielsen
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M φ M ψ $M_{\varphi}M_{\psi}$ -convexity and separation theorems
Journal of Inequalities and Applications, 2022 A characterization of pairs of functions that can be separated by an M φ M ψ $M_{\varphi}M_{\psi}$ -convex function and related results are obtained. Also, a Hyers–Ulam stability result for M φ M ψ $M_{\varphi}M_{\psi}$ -convex functions is given.
Mea Bombardelli, Sanja Varošanec
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Inequalities on several quasi-arithmetic means
Tamkang Journal of Mathematics, 2012 Inequalities on several quasi-arithmetic means are established by using convexity and concavity.
Shuoh-Jung Liu +2 more
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The multivariate arithmetic Tutte polynomial [PDF]
, 2012 We introduce an arithmetic version of the multivariate Tutte polynomial, and (for representable arithmetic matroids) a quasi-polynomial that interpolates between the two.
Brändén, Petter, Moci, Luca
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Kufa Journal for Nursing Sciences, 2021 Background: A peripheral intravenous cannula is an essential tool for delivering drugs, blood products, and nutritional fluids to patients intravenously.
Karrar F. Al-Naeli, Hakima Hassan
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On the Composition of Homogeneous Quasi-Arithmetic Means
Journal of Mathematical Analysis and Applications, 1997 It is well known [e.g., \textit{G. H. Hardy, J. E. Littlewood}, and \textit{G. Pólya}, ``Inequalities'' (1934; Zbl 0010.10703, 2nd ed. 1952; Zbl 0047.05302, reprint of the 2nd ed. 1988; Zbl 0634.26008), Theorem 84] that the power means \(M_{p}\) (including the geometric mean for \(p=0\)) are the only positively homogeneous quasiarithmetic means.
Kahlig, Peter, Matkowski, Janusz
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