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A functional equation with a symmetric binary operation

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Abstract

Let X be a nonempty set containing at least two elements and let \({\circ :X^2\to X}\) be a symmetric binary operation. Furthermore, let A, B, C be real parameters and let \({f,g:X\to\mathbb{R}_+}\) be unknown functions. We investigate the functional equation

$$f(x\circ y)[Ag(y)-Bg(x)]=(A+C)f(x)g(y)-(B+C)f(y)g(x)\quad {\rm for\,\,all}\,x,y \in X.$$

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, P. O. Box 12, 4010, Debrecen, Hungary

    Zoltán Daróczy

  2. Mathematics Research Unit, Campus Kirchberg, University of Luxembourg, BLG, 6, rue Richard Coudenhove-Kalergi, 1359, Luxembourg, Grand Duchy of Luxembourg

    Judita Dascăl

Authors
  1. Zoltán Daróczy
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  2. Judita Dascăl
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Corresponding author

Correspondence to Judita Dascăl.

Additional information

Dedicated to Professor Janusz Matkowski on the occasion of his seventieth birthday

This research has been supported by the Hungarian Scientific Research Fund (OTKA) Grant NK 81402.

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Daróczy, Z., Dascăl, J. A functional equation with a symmetric binary operation. Aequat. Math. 82, 291–297 (2011). https://doi.org/10.1007/s00010-011-0095-9

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  • DOI: https://doi.org/10.1007/s00010-011-0095-9

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