Results 191 to 200 of about 77,751 (215)
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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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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, 2008The 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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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 +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 +2 more
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On Means That are Both Quasi-Arithmetic and Conjugate Arithmetic
Acta Mathematica Hungarica, 2001The 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
2010In 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, 2010The 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
2013In 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 +2 more
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Matkowski–Sutô Type Equation on Symmetrized Weighted Quasi-Arithmetic Means
Results in Mathematics, 2011Given \(\varphi \in \mathcal{CM}(I)\) (\(\mathcal{CM}(I)\) is the class of continuous and strictly monotone real valued functions defined on the open interval \(I\)), \(A_{\varphi}(x,y;\alpha)\) denotes the weighted quasi-arithmetic mean generated by \(\varphi\) with weight \(\alpha ...
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Investigations on quasi-arithmetic means for machine condition monitoring
Mechanical Systems and Signal Processing, 2021Bingchang Hou, Dong Wang, Tangbin Xia
exaly