On some orthogonally additive functions on inner product spaces. (English) Zbl 1289.39049
Summary: Let \(E\) be a real inner product space of dimension at least 2. If \(f : E\to E\) satisfies
\[
f(x + y) = f(x) + f(y) \quad \text{for all orthogonal}\;x, y \in E
\]
and
\[
f(f(x)) = x\quad \text{for}\;x \in E,
\]
then \(f\) is additive.
MSC:
| 39B55 | Orthogonal additivity and other conditional functional equations |
| 39B12 | Iteration theory, iterative and composite equations |
| 46C99 | Inner product spaces and their generalizations, Hilbert spaces |
