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Date:
08 May 2010
On an equation involving weighted quasiarithmetic means
 J. Jarczyk
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Let I ⊂ ℝ be an interval and κ, λ ∈ ℝ / {0, 1}, µ, ν ∈ (0, 1). We find all pairs (φ, ψ) of continuous and strictly monotonic functions mapping I into ℝ and satisfying the functional equation
$$
\kappa x + (1  \kappa )y = \lambda \phi ^{  1} (\mu \phi (x) + (1  \mu )\phi (y)) + (1  \lambda )\psi ^{  1} (\nu \psi (x) + (1  \nu )\psi (y))
$$
 Title
 On an equation involving weighted quasiarithmetic means
 Journal

Acta Mathematica Hungarica
Volume 129, Issue 12 , pp 96111
 Cover Date
 201010
 DOI
 10.1007/s104740109246z
 Print ISSN
 02365294
 Online ISSN
 15882632
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 mean
 functional equation
 quasiarithmetic mean
 invariant mean
 regularity of solutions
 primary 26E60
 secondary 39B22
 Authors

 J. Jarczyk ^{(1)}
 Author Affiliations

 1. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, PL65516, Zielona Góra, Poland