Summary.
Let \( \phi,\psi : {\Bbb R } \to {\Bbb R} \) be given functions, such that \( \phi \) is continuous and \( |\psi(1)| \neq 1 \). We solve the functional equation¶\( f(x \phi[f(y)] + y \psi[f(x)]) = f(x)f(y) \qquad {\rm for}\,x,y \in {\Bbb R} \)¶in the class of continuous functions \( f : {\Bbb R} \to {\Bbb R} \).¶In particular we give the forms of \( \phi,\psi \) for which the equation has non-constant solutions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: August 14, 1998; revised version: March 8, 2000.
Rights and permissions
About this article
Cite this article
Chudziak, J. Continuous solutions of a generalization of the Gołąb-Schinzel equation. Aequ. math. 61, 63–78 (2001). https://doi.org/10.1007/s000100050161
Issue Date:
DOI: https://doi.org/10.1007/s000100050161