On the equation of the $\rho$-orthogonal additivity

Claudi Alsina, Justyna Sikorska, and Maria Santos Tomás. "On the equation of the $\rho $-orthogonal additivity." Commentationes Mathematicae 47.2 (2007): null. <http://eudml.org/doc/291402>.

@article{ClaudiAlsina2007,
abstract = {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 $(X, \Vert · \Vert )$ with $\text\{dim\} X \ge 2$ into an abelian group $(G, +)$ and $\perp ^\rho $ is a given orthogonality relation associated to the norm.},
author = {Claudi Alsina, Justyna Sikorska, Maria Santos Tomás},
journal = {Commentationes Mathematicae},
keywords = {Cauchy functional equation; quadratic functional equation; orthogonally additive function; orthogonally quadratic function; Birkhoff orthogonality; smooth spaces},
language = {eng},
number = {2},
pages = {null},
title = {On the equation of the $\rho $-orthogonal additivity},
url = {http://eudml.org/doc/291402},
volume = {47},
year = {2007},
}

TY - JOUR
AU - Claudi Alsina
AU - Justyna Sikorska
AU - Maria Santos Tomás
TI - On the equation of the $\rho $-orthogonal additivity
JO - Commentationes Mathematicae
PY - 2007
VL - 47
IS - 2
SP - null
AB - 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 $(X, \Vert · \Vert )$ with $\text{dim} X \ge 2$ into an abelian group $(G, +)$ and $\perp ^\rho $ is a given orthogonality relation associated to the norm.
LA - eng
KW - Cauchy functional equation; quadratic functional equation; orthogonally additive function; orthogonally quadratic function; Birkhoff orthogonality; smooth spaces
UR - http://eudml.org/doc/291402
ER -