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We analyse the functional equation $$\begin{aligned} f(x)+f(y)=\max \{f(xy),f(xy^{-1})\} \end{aligned}$$f(x)+f(y)=max{f(xy),f(xy-1)}for a function $$f:G\rightarrow \mathbb R$$f:G→R where G is a group. Without further assumption it characterises the absolute value of additive functions.… Click to show full abstract
We analyse the functional equation $$\begin{aligned} f(x)+f(y)=\max \{f(xy),f(xy^{-1})\} \end{aligned}$$f(x)+f(y)=max{f(xy),f(xy-1)}for a function $$f:G\rightarrow \mathbb R$$f:G→R where G is a group. Without further assumption it characterises the absolute value of additive functions. In addition $$\{z\in G\mid f(z)=0\}$${z∈G∣f(z)=0} is a normal subgroup of G with abelian factor group.
Keywords:
varvec varvec;
varvec;
functional equation;
max;
equation varvec
Journal Title: Archiv der Mathematik
Year Published: 2017
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Journal Title: Archiv der Mathematik
Year Published: 2017
Link to full text (if available)
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recommendations!