An Elementary Proof of Surjectivity for a Class of Accretive Operators
William O. Ray · Proceedings of the American Mathematical Society · 1979
An operator A defined on a real Banach space X is said to be locally accretive if, for each $\lambda > 0,x \in X$ and each y near x, $x,\left \| {x - y} \right \| \leqslant \left \| {x - y + \lambda (Ax - Ay)} \right \|$. It is shown that if $A:X \to X$ is locally accretive and locally Lipschitzian then $(I + A)(X) = X$.