2Faculty of Sciences, IBN TOFAIL University , KENITRA, MOROCCO.
Abstract. Let X be a vector space over a ﬁeld K of real or complex numbers. We will prove the superstability of the following Golab-Schinzel type equation f(x + g(x)y) = f(x)f(y); x; y 2 X; where f; g are unknown functions (satisfying some assumptions). Then we generalize the superstability result for this equation with values in the ﬁeld of complex numbers to the case of an arbitrary Hilbert space with the Hadamard product. Our result refers to papers by Chudziak and Tabor (J. Math. Anal. Appl. 302 (2005) 196–200), Jab lo´nska (Bull. Aust. Math. Soc. 87 (2013), 10–17) and Rezaei (Math. Ineq. Appl., 17 (2014), 249–258).