The aim of this paper is to characterize the solutions Φ:G→M2(ℂ) of the following matrix functional equations
\frac{Φ(xy)+Φ(σ(y)x)}{2} = Φ(x)Φ(y), x,y∈G,
and
\frac{Φ(xy)-Φ(σ(y)x)}{2} = Φ(x)Φ(y), x,y∈G,
where G is a group that need not be abelian, and σ:G→G is an involutive automorphism of G. Our considerations are inspired by the papers [13, 14] in which the continuous solutions of the first equation on abelian topological groups were determined.
English