Abstract
In the present paper, we prove the stability of the functional equation \[ \max\{f((x\circ y)\circ y),f(x)\}=f(x\circ y)+f(y) \] for real valued functions defined on a square-symmetric groupoid with a left unit element. As a consequence, we obtain the known result about the stability of the equation \[ \max\{f(x+y),f(x-y)\}=f(x)+f(y) \] for real valued functions defined on an abelian group.
Citation
Attila Gilányi. Kaori Nagatou. Peter Volkmann. "Stability of a functional equation coming from the characterization of the absolute value of additive functions." Ann. Funct. Anal. 1 (2) 1 - 6, 2010. https://doi.org/10.15352/afa/1399900582
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