On an orthogonality equation in normed spaces (Q1755984)

The concepts of Birkhoff orthogonality and norm derivatives are important in studying the geometry of normed spaces. The article under review explores the linearity properties of mapping preserving norm derivatives, in the setting of normed spaces. The author illustrates that a surjective mapping between a real Banach space and a separable real Banach space that satisfies a related functional equation, must be linear. The question is also treated under additional geometric assumptions like strict convexity and smoothness of the respective Banach spaces, to prove the existence of nonlinear mappings satisfying the same functional equation. In the view of the reviewer, the concerned article is a nice addition to the existing geometric theory of normed spaces.