Let X and Y  be real vector spaces, m a fixed positive integer, a a real number with \(a > 1\) , and let \(i_1, i_2, \ldots , i_m\) be real numbers with \(i_1 < i_2 < \cdots < i_m\) . In this paper, we present a method to express each mapping as a sum of mappings with a familiar property. More precisely, we prove that a mapping \(f : X \to Y\) can be expressed as the sum of the mappings \(f_1, f_2, \ldots , f_m : X \to Y\) which have the property \(f_k(ax) = a^{i_k} f_k(x)\) for all \(k \in \{ 1, 2, \ldots , m \}\) if and only if \(f(x)\) is a solution to the functional equation (2.3). In particular, we prove that each \(f_k(x)\) can be expressed as a linear combination of \(f(x), f(ax), \ldots , f(a^{m-1} x)\) .