The mapping $y = u(x) + p(x)$ of a Banach space $X$ into Banach space $Y$ is considered. A theorem by L.M. Graves ensures the existence of a solution of the equation $y = u(x) + p(x)$ for fixed $y$ without assuming the existence of $u^{-1}$. Theorem 1 of this paper generalizes such a result; theorem 2 gives a condition for the uniqueness.