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On the Stability of Orthogonal Additivity

100%

Fechner W. , Sikorska J.

tom 58

nr 1

23-30

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.

On the equation of the \(\rho\)-orthogonal additivity

80%

Alsina C. , Sikorska J. , Santos Tomás M.

Commentationes Mathematicae

2007

tom 47

nr 2

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.