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On the Stability of Orthogonal Additivity

Włodzimierz Fechner; Justyna Sikorska — 2010

Bulletin of the Polish Academy of Sciences. Mathematics

We deal with the stability of the orthogonal additivity equation, presenting a new approach to the proof of a 1995 result of R, Ger and the second author. We sharpen the estimate obtained there. Moreover, we work in more general settings, providing an axiomatic framework which covers much more cases than considered before by other authors.

Note on a functional equation related to the power means.

Sikorska, Justyna — 2000

Mathematica Pannonica

Generalized orthogonal stability of some functional equations.

Sikorska, Justyna — 2006

Journal of Inequalities and Applications [electronic only]

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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