Abstract
We analyse the functional equation
for a function \(f:G\rightarrow \mathbb R\) where G is a group. Without further assumption it characterises the absolute value of additive functions. In addition \(\{z\in G\mid f(z)=0\}\) is a normal subgroup of G with abelian factor group.
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Toborg, I. On the functional equation \({\varvec{f}}({\varvec{x}})+{\varvec{f}}({\varvec{y}})=\mathbf{max} \{{\varvec{f}}({\varvec{xy}}),{\varvec{f}}({\varvec{xy}}^{-{\varvec{1}}})\}\) on groups. Arch. Math. 109, 215–221 (2017). https://doi.org/10.1007/s00013-017-1061-0
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DOI: https://doi.org/10.1007/s00013-017-1061-0