On the system of the Abel equations on the plane - Leśniak, Zbigniew (Annales Mathematicae Silesianae, 1995)
We find all of continuous, homeomorphic and Ck solutions of the system of the Abel equations ϕ(f(x)) = ϕ(x)+a ϕ(g(x)) = ϕ(x)+b for x∈ℝ2, where a,b are linearly independent vectors and f,g are commutable orientation preserving homeomorphisms of the plane onto itself satisfying some condition which is equivalent to the fact that there exists a homeomorphic solution of the system above.