On the functional equation $${\varvec{f}}({\varvec{x}})+{\varvec{f}}({\varvec{y}})=\mathbf{max} \{{\varvec{f}}({\varvec{xy}}),{\varvec{f}}({\varvec{xy}}^{-{\varvec{1}}})\}$$f(x)+f(y)=max{f(xy),f(xy-1)} on groups
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DOI: 10.1007/s00013-017-1061-0
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}… read more here.
Keywords: varvec varvec; varvec; functional equation; max ... See more keywords