Results 191 to 200 of about 77,460 (224)

Quasi-Arithmetic Means

2003
The power means are defined using the convex, or concave, power, logarithmic and exponential functions. In this chapter means are defined using arbitrary convex and concave functions by a natural extension of the classical definitions and analogues of the basic results of the earlier chapters are investigated.
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On the equality of generalized quasi-arithmetic means

Publicationes Mathematicae Debrecen, 2008
The classical equality problem is discussed in the class of means \(M_{\varphi, \mu}:I^{2}\to \mathbb{R}\) defined by \[ M_{\varphi, \mu}(x,y)=\varphi^{-1}\left(\int_{0}^{1}\varphi(tx+(1-t)y)d\mu(t)\right) \qquad (x,y \in I) \] where \(I\) is a nonempty open real interval, \(\varphi:I\to \mathbb{R}\) is a given continuous and strictly monotone function
Makó, Zita, Páles, Zsolt
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An Orness Measure for Quasi-Arithmetic Means

IEEE Transactions on Fuzzy Systems, 2006
In this paper, an orness measure to reflect the or-like degree of the quasi-arithmetic mean operator is proposed. With the generating function representation method, some properties of a quasi-arithmetic mean, associated with its orness measure, are analyzed.
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On linear combinations of weighted quasi-arithmetic means

Aequationes mathematicae, 2005
Let \(CM(I)\) denote the set of all continuous and strictly monotone real functions on the interval \(I\). A mean \(M\) on \(I\) is called a weighted quasi--arithmetic mean if there exists \(\phi \in CM(I)\) such that \[ M(x,y)=\phi^{-1}(\lambda\phi(x)+(1-\lambda)\phi(y))=:A_{\phi}(x,y;\lambda) \qquad (x,y \in I).
Daróczy, Zoltán, Hajdu, Gabriella
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Order among quasi-arithmetic means of positive operators [PDF]

Mathematical Reports, 2012
As a continuation of our previous research [J. Mićić, J. Pečarić and Y. Seo, Converses of Jensen's operator inequality, Oper. Matrices, 4 (2010) 385-403], we discuss order among quasi-arithmetic means of positive operators with fields of positive linear mappings (phi_t)_{;t\in T}; such that \int_T phi_t(1) = k for some positive scalar k.
Mićić, Jadranka, Pečarić, Josip, Seo, Yuki   +2 more
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Jensen type inequalities on quasi-arithmetic operator means [PDF]

Scientiae Mathematicae Japonicae, 2011
As a continuation of our previous considerations about the operator order among quasi-arithmetic means [Linear Algebra Appl. 434 (2011), 1228-1237], we study this order with a di erent condition on the spectra. As an application we gave the order among some means. Also, we give similar results for F-order.
Mićić Hot, Jadranka, Pečarić, Josip, Pavić, Zlatko   +2 more
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On Means That are Both Quasi-Arithmetic and Conjugate Arithmetic

Acta Mathematica Hungarica, 2001
The authors determine all means of two variables that are simultaneously of the form \[ \psi^{-1}\biggl({\psi(x)+\psi(y)\over 2}\biggr)\quad\text{and}\quad \varphi^{-1}(\varphi(x)+\varphi(y)-\varphi\Bigl({x+y\over 2}\Bigl)). \] The functions \(\psi\) and \(\varphi\) are strictly monotonic, continuous, defined on an open real interval, and one of them ...
Daróczy, Z., Páles, Zs.
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Weighted Quasi-arithmetic Means and Conditional Expectations

2010
In this paper, the weighted quasi-arithmetic means are discussed from the viewpoint of utility functions and background risks in economics, and they are represented by weighting functions and conditional expectations. Using these representations, an index for background risks in stochastic environments is derived through the weighted quasi-arithmetic ...
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On an equation involving weighted quasi-arithmetic means

Acta Mathematica Hungarica, 2010
The main theorem of this paper gives a full solution of the Matkowski-Sutô type functional equation \[ \kappa x+(1-\kappa)y=\lambda \varphi^{-1}(\mu\varphi(x)+(1-\mu)\varphi(y)) +(1-\lambda)\psi^{-1}(\nu\psi(x)+(1-\nu)\psi(y)). \] The unknown functions \(\varphi\) and \(\psi\) are assumed to be continuous and strictly monotone on an interval (these are
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Refining some inequalities involving quasi- arithmetic means

2013
In this paper we re ne some inequalities involving quasi-arithmetic means for a continuous eld of self-adjoint operators, a eld of positive linear mappings and continuous strictly monotone functions which induce means. New re ned converses are presented by using the Mond-Pe cari c method improvement.
Hot, Kemal, Pečarić, Josip, Mićić Hot, Jadranka   +2 more
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