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On the equation of the $ρ$ -orthogonal additivity

Claudi Alsina; Justyna Sikorska; Maria Santos Tomás — 2007

Commentationes Mathematicae

We solve a conditional functional equation of the form $x ⊥^{ρ} y \Rightarrow f (x + y) = f (x) + f (y),$ where $f$ is a mapping from a real normed linear space $(X, ∥ \cdot ∥)$ with $dim X \geq 2$ into an abelian group $(G, +)$ and $⊥^{ρ}$ is a given orthogonality relation associated to the norm.

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On the equation of the ρ -orthogonal additivity

On the equation of the $ρ$ -orthogonal additivity