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Remarks concerning the pexiderized Gołąb-Schinzel functional equation

Jabłońska E.

Journal of Mathematics and Applications

2012

Vol. 35

33--38

This paper is devoted to proof of theorem concerning solutions of the pexiderized Gołąb-Schinzel functional equation. We provide explicite formulas expressing solutions of the equation. Our considerations refer to the paper [6].

Bounded solutions of a generalized Gołąb-Schinzel equation

Jabłońska E.

Demonstratio Mathematica

2009

Vol. 42, nr 3

533-547

Let X be a linear space over the field K of real or complex numbers. We characterize solutions f : X - > K and M : K - > K of the equation f(x+M)(f)y)=f(x)f(y) in the case where the set {x is an element of X : f (x) = 0} has an algebraically interior point. As a consequence we give solutions of the equation such that f is bounded on this set.