Jensen, multi-Jensen and polynomial functions on arbitrary Abelian groups (Q623410)

Assume that \(G,H\) are abelian groups. A function \(f:G\to H\) is called \textit{modified Jensen function}, if, for all elements \(x,y,z\in G\), it satisfies the functional equation \[ f(x+y-z)=f(x)+f(y)-f(z). \] Let \(G_1,\dots,G_n,H\) be abelian groups. Then \(f:G_1\times\cdots\times G_n\to H\) is said to be a \textit{modified multi-Jensen function} if it has the modified Jensen property in each variable. Using algebraic and combinatorial methods, the authors give characterizations for a function to be a modified Jensen and a modified multi-Jensen one, respectively. At last, they place multi-Jensen and symmetric multi-Jensen functions into the context of polynomial functions acting on abelian groups.