Opuscula Math. 29, no. 4 (2009), 423-425

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
  • Received: 2009-08-11.
  • Revised: 2009-08-18.
  • Accepted: 2009-08-21.
Opuscula Mathematica - cover

Cite this article as:
Janusz Matkowski, Extensions of solutions of a functional equation in two variables, Opuscula Math. 29, no. 4 (2009), 423-425, http://dx.doi.org/10.7494/OpMath.2009.29.4.423

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