• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.387-398
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• 2016

Let X be a vector space over a field K of real or complex numbers and $k{\in}{\mathbb{N}}$. We prove the superstability of the following generalized Golab-Schinzel type equation $f(x_1+{\limits\sum_{i=2}^p}x_if(x_1)^kf(x_2)^k{\cdots}f(x_{i-1})^k)={\limits\prod_{i=1}^pf(x_i),x_1,x_2,{\cdots},x_p{\in}X$, where $f:X{\rightarrow}K$ is an unknown function which is hemicontinuous at the origin.