Results 131 to 140 of about 117,185 (161)
Some of the next articles are maybe not open access.
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
openaire +1 more source
A functional equation involving comparable weighted quasi-arithmetic means
Acta Mathematica Hungarica, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daróczy, Z., Maksa, Gy.
openaire +2 more sources
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
openaire +1 more source
Multivariable interpolation by weighted arithmetic means at arbitrary points
Calcolo, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Allasia, G. +2 more
openaire +2 more sources
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 ...
openaire +1 more source
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 ...
openaire +2 more sources
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,
openaire +2 more sources
WEIGHTED QUASI-ARITHMETIC MEANS AND A RISK INDEX FOR STOCHASTIC ENVIRONMENTS
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2011In this paper, the weighted quasi-arithmetic means are discussed from the viewpoint of utility functions and downward risks in economics. Representing the weighting functions by probability density functions and the conditional expectations, an index for downward risks in stochastic environments is derived.
openaire +1 more source
, 2022