×

Stability of a functional equation coming from the characterization of the absolute value of additive functions. (English) Zbl 1219.39014

Let \((S,\circ)\) be a square-symmetric groupoid, i.e, \((x\circ y)\circ(x\circ y)=(x\circ x)\circ(y\circ y)\) for each \(x,y\in S\). The authors investigate the stability of the functional equation \[ \max \{f((x \circ y)\circ y), f(x)\}=f(x \circ y)+f(y), \] where \(f:S\to \mathbb R\) is a real valued function and \(S\) is a square-symmetric groupoid with a left unit element.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)
PDFBibTeX XMLCite
Full Text: DOI EuDML EMIS