Functions having the Darboux property and satisfying some functional equation
Volume 114 / 2009
Colloquium Mathematicum 114 (2009), 113-118
MSC: 39B52, 26A30.
DOI: 10.4064/cm114-1-9
Abstract
Let $X$ be a real linear topological space. We characterize solutions $f:X\rightarrow\mathbb{R}$ and $M:\mathbb{R}\rightarrow \mathbb{R}$ of the equation $f(x+M(f(x))y)=f(x)f(y)$ under the assumption that $f$ and $M$ have the Darboux property.
