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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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1988
The power means n [r] (a;w), reR, defined in the previous chapter can be looked at in the following way; for each reR define a function φ as follows: Φ(x) = xr, r ≠ 0, Φ(x) = log x, r = 0, then $$M_n^{[r]}(\underline a ;\underline w ) = {\phi ^{ - 1}}\quad (\frac{1}{{{w_n}}}\sum\limits_{i = 1}^n {{w_i}\;\phi ({a_i})} ).$$ (1) This suggests ...
P. S. Bullen +2 more
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The power means n [r] (a;w), reR, defined in the previous chapter can be looked at in the following way; for each reR define a function φ as follows: Φ(x) = xr, r ≠ 0, Φ(x) = log x, r = 0, then $$M_n^{[r]}(\underline a ;\underline w ) = {\phi ^{ - 1}}\quad (\frac{1}{{{w_n}}}\sum\limits_{i = 1}^n {{w_i}\;\phi ({a_i})} ).$$ (1) This suggests ...
P. S. Bullen +2 more
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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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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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The Matkowski–Sutő problem for weighted quasi-arithmetic means
Acta Mathematica Hungarica, 2003Let \(I\subset\mathbb{R}\) be a non-void open interval and let \(\mathcal{CM}(I)\) denote the class of all continuous and strictly monotone real-valued functions defined on the interval \(I\). A function \(M:I\times I \to I\) is called a weighted quasi-arithmetic mean on \(I\) if there exist a number ...
Daróczy, Z., Páles, Zs.
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On the Max-quasi-Arithmetic Mean Powers of a Fuzzy Matrix
2009 International Joint Conference on Computational Sciences and Optimization, 2009Since Thomason's paper in 1977 showing that the max-min powers of a fuzzy matrix either converge or oscillate with a finite period, many different algebraic operations are employed to explore the limiting behavior of powers of a fuzzy matrix, such as max-min/max-product/max-Archimedean t-norm/max-t-norm/max-arithmetic mean operations.
Yung-Yih Lur +3 more
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Invariant and complementary quasi-arithmetic means
Aequationes Mathematicae, 1999If \(I\) is a proper (non-singleton) real interval and \(M\) and \(N\) are continuous, both map \(I^{2}\) into \(I\), and both \(M(x,y)\) and \(N(x,y)\) lie between \(\min(x,y)\) and \(\max(x,y),\) one of them always strictly between if \(x\neq y\) (that is, both are means and one of them is a strict mean), then it is easy to see that there exists a ...
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Invariance equation for generalized quasi-arithmetic means
Aequationes mathematicae, 2009In this paper, the invariance equation $$(\varphi_{1} + \varphi_{2})^{-1} (\varphi_{1}(x) + \varphi_{2}(y)) + (\psi_{1} + \psi_{2})^{-1}(\psi_{1}(x) + \psi_{2}(y)) = x + y$$ is solved under four times continuous differentiability of the unknown functions φ1, φ2, ψ1, ψ2.
Szabolcs Baják, Zsolt Páles
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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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Investigations on quasi-arithmetic means for machine condition monitoring
Mechanical Systems and Signal Processing, 2021Bingchang Hou, Dong Wang, Tangbin Xia
exaly