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CONTINUOUS ON RAYS SOLUTIONS OF A GOŁA̧B–SCHINZEL TYPE EQUATION
Published online by Cambridge University Press: 15 December 2014
Abstract
We show that if the pair $(f,g)$ of functions mapping a linear space
$X$ over the field
$\mathbb{K}=\mathbb{R}\text{ or }\mathbb{C}$ into
$\mathbb{K}$ satisfies the composite equation
$$\begin{eqnarray}f(x+g(x)y)=f(x)f(y)\quad \text{for }x,y\in X\end{eqnarray}$$
$f$ is nonconstant, then the continuity on rays of
$f$ implies the same property for
$g$. Applying this result, we determine the solutions of the equation.
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- Copyright © 2014 Australian Mathematical Publishing Association Inc.
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