Results 11 to 20 of about 4,336,501 (199)
On the Equality of Bajraktarević Means to Quasi-Arithmetic Means [PDF]
Results in Mathematics, 2019 AbstractThis paper offers a solution of the functional equation$$\begin{aligned}&\big (tf(x)+(1-t)f(y)\big )\varphi (tx+(1-t)y)\\&\quad =tf(x)\varphi (x)+(1-t)f(y)\varphi (y) \qquad (x,y\in I), \end{aligned}$$(tf(x)+(1-t)f(y))φ(tx+(1-t)y)=tf(x)φ(x)+(1-t)f(y)φ(y)(x,y∈I),where$$t\in \,]0,1[\,$$t∈]0,1[,$$\varphi :I\rightarrow \mathbb {R}$$φ:I→Ris ...
Zsolt Páles, Amr Zakaria
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On approximating the quasi-arithmetic mean [PDF]
Journal of Inequalities and Applications, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tie-Hong Zhao +3 more
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Quasi-Arithmetic Means Ad Libitum
Results in Mathematics, 2023 AbstractLet $$\alpha _1, \ldots , \alpha _m$$ α 1 , … , α m be two ...
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CoRR, 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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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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Characterization of generalized quasi-arithmetic means [PDF]
Acta Scientiarum Mathematicarum, 2015 In this paper we characterize generalized quasi-arithmetic means, that is means of the form $M(x_1,...,x_n):=(f_1+...+f_n)^{-1}(f_1(x_1)+...+f_n(x_n))$, where $f_1,...,f_n:I\to\mathbb{R}$ are strictly increasing and continuous functions. Our characterization involves the Gauss composition of the cyclic mean-type mapping induced by $M$ and a generalized
Matkowski, Janusz, Páles, Zsolt
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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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Some Mean Values Related to the Quasi-Arithmetic Mean
Journal of Mathematical Analysis and Applications, 2000 Let \(p:\mathbb{R}^{+}\rightarrow \mathbb{R}\) be a strictly monotonic function, \(H\) denote the harmonic mean, \(r\) a real number in \([0,1],\) and \[ t_{n}(\theta)=\left( a^{2n}\cos ^{2}\theta +b^{2n}\sin ^{2}\theta \right) ^{1/n} \quad (n\neq 0). \] The authors study mean values defined by the expressions: \[ M(a,b;p,t_{n})=\frac{1}{H(a,b)}p^{-1 ...
Ume, Jeong Sheok, Kim, Young-Ho
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An estimate of quasi-arithmetic mean for convex functions
Scientiae Mathematicae Japonicae, 2012 For a selfadjoint operator A on a Hilbert space H and a normalized positive linear map Phi, a quasi-arithmetic mean is defined by phi^-1(Phi(phi(A)) for a strictly monotone function phi. In this paper, we shall show an order relation among quasi-arithmetic means for convex functions through positive linear maps and its complementary problems, in which ...
Hot, Jadranka Mi´ci´c +2 more
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Advanced Engineering Materials, EarlyView.Binder‐free laser powder bed fusion of 8YSZ with a femtosecond laser is used to map process windows linking scan strategy, heat accumulation, and grain growth. Time‐resolved thermography and simulations reveal thermal regimes that enable continuous, vitrified, and fine‐grained 8YSZ surface layers without absorptive additives and demonstrate ...
Markus Kühn +5 more
wiley +1 more source