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

Claudi Alsina; Justyna Sikorska; Maria Santos Tomás

Commentationes Mathematicae (2007)

- Volume: 47, Issue: 2
- ISSN: 2080-1211

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topClaudi 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 -

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