Solution of Whitehead equation on groups. (English) Zbl 1289.39047
The authors study the solutions of the Whitehead functional equation
\[
f(xyz) + f(x) + f(y) + f(z) = f(xy) + f(xz) + f(yz),
\]
where the function \(f\) is defined on a group and takes its values in an abelian group. The solutions of the Fréchet functional equation
\[
f(xyz) + f(x) + f(y) + f(z) = f(xy) + f(zx) + f(yz)
\]
under the same conditions are also investigated. For the description of the solutions the authors use standard methods, reducing the equations to Jensen and quadratic equations.
Reviewer: László Székelyhidi (Debrecen)
MSC:
39B52 | Functional equations for functions with more general domains and/or ranges |