Decomposition of functional equations with applications

Abstract

In this paper the Decomposition Theorem for functional equations is shown. As an application of this Theorem the two times continuously differentiable solution of the functional equation G 1 (x(x + y)) + F 1 (y) = G 2 (y(x + y)) + F 2 (y) can be given with unknown functions G i , F i : R + → R (i = 1, 2) where the Equation is fulfilled for all x, y ∈ R + (where R + := {x ∈ R | x > 0}).