Opuscula Math. 29, no. 4 (2009), 423-425
http://dx.doi.org/10.7494/OpMath.2009.29.4.423

Opuscula Mathematica

# Extensions of solutions of a functional equation in two variables

Janusz Matkowski

Abstract. An extension theorem for the functional equation of several variables $f(M(x,y))=N(f(x),f(y)),$ where the given functions $$M$$ and $$N$$ are left-side autodistributive, is presented.

Keywords: functional equation, autodistributivity, strict mean, extension theorem.

Mathematics Subject Classification: 39B22.

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• Janusz Matkowski
• University of Zielona Góra, Institute of Mathematics, Computer Science and Econometrics, ul. Podgórna 50, 65-246 Zielona Góra, Poland
• Silesian University, Institute of Mathematics, 40-007 Katowice, Poland
• Revised: 2009-08-18.
• Accepted: 2009-08-21.