Geodesic
On the equation of the \(\rho\)-orthogonal additivity
Commentationes Mathematicae, Tome 47 (2007) no. 2, pp. 171-178.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

We solve a conditional functional equation of the form \[ x \perp^{\rho} y\Rightarrow f (x + y) = f (x) + f (y), \] where \(f\) is a mapping from a real normed linear space \((X, \| · \|)\) with \(\text{dim} X \geq 2\) into an abelian group \((G, +)\) and \(\perp^\rho\) is a given orthogonality relation associated to the norm.
DOI : 10.14708/cm.v47i2.5247
Mots-clés : Cauchy functional equation, quadratic functional equation, orthogonally additive function, orthogonally quadratic function, Birkhoff orthogonality, smooth spaces 
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Claudi Alsina; Justyna Sikorska; Maria Santos Tomás. On the equation of the \(\rho\)-orthogonal additivity. Commentationes Mathematicae, Tome 47 (2007) no. 2, pp.  171-178. doi : 10.14708/cm.v47i2.5247. http://geodesic.mathdoc.fr/articles/10.14708/cm.v47i2.5247/

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