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Generalized Weighted Arithmetic Means
2011Means which are the sum of single variable functions are considered. It is shown among other that if such a mean is weighted quasi-arithmetic, or subtranslative or subadditive then it must be a weighted quasi-arithmetic mean. Conditions under which the functions of the form f(x) = ax + b are affine or convex with respect to such a mean are presented ...
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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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Weighted Quasi-Arithmetic Means: Utility Functions and Weighting Functions
2013This paper discusses weighted quasi-arithmetic means from viewpoint of a combined index of utility functions and weighting functions, which represent stochastic risk in economics. The combined index characterizes decision maker's attitude and background risks in stochastic environments by conditional expectation representations of weighted quasi ...
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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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On a Functional Equation Containing Weighted Arithmetic Means
2008In this paper we solve the functional equation $$ \sum\limits_{i = 1}^n {a_i f(\alpha _i x + (1 - \alpha _i )y) = 0} $$ which holds for all x, y ∈ I, where I ⊂ ℝ is a non-void open interval, f : I → ℝ is an unknown function and the weights αi ∈ (0, 1) are arbitrarily fixed (i = 1, . . ., n).
Adrienn Varga, Csaba Vincze
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Multivariable interpolation by weighted arithmetic means at arbitrary points
Calcolo, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Allasia, G. +2 more
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Weighted arithmetic means possessing 0 the interpolation property
Calcolo, 1988A method to construct a wide class of weighted arithmetic means, possessing the interpolation property, is proposed. The approximation problem of a continuous real function by these interpolating mean functions is examined. A few examples are given and include the Shepard formula and the classical Hermite-Fejer formula.
G. Allasia, R. Besenghi, V. Demichelis
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Invariance of weighted quasi-arithmetic means with continuous generators
Publicationes Mathematicae Debrecen, 2007The paper is a significant contribution to the theory of the invariance equation \[ M_0\big(M_1(x,y),M_2(x,y)\big)=M_0(x,y),\qquad(x,y\in I), \] where \(M_0,M_1,M_2:I^2\to I\) are two-variable means on the interval \(I\). The main result of the paper completely solves this equation in the class of weighted two-variable quasiarithmetic means (i.e, when,
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Weighted Quasi-Arithmetic Mean on Two-Dimensional Regions and Their Applications
2015This paper discusses a decision maker’s attitude regarding risks, for example risk neutral, risk averse and risk loving in micro-economics by the convexity and concavity of utility functions. Weighted quasi-arithmetic means on two-dimensional regions are introduced, and some conditions on utility functions are discussed to characterize the decision ...
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