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aequationes mathematicae

, Volume 71, Issue 3, pp 288–293 | Cite as

A remark on solutions of a generalization of the addition formulae

  • Janusz Brzdek
Original Paper

Summary.

Let J be a real interval and \( H:\mathbb{R}^2 \to \mathbb{R} \). Under some assumptions we determine all continuous functions \( g:\mathbb{R} \to J \) and \( M:J \to \mathbb{R} \) satisfying the equation
$$ g\left( {x + M\left( {g\left( x \right)} \right)y} \right) = H\left( {g\left( x \right),g\left( y \right)} \right). $$
We also show some consequences of this result.

Mathematics Subject Classification (2000).

39B12 39B22 

Keywords.

Addition formula Gołab–Schinzel functional equation 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of MathematicsPedagogical UniversityKrakówPoland

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