Theorem. On Hilbert space $V$, suppose $T: V \to V$ is nonlinear and that $T = A + \tau B$ where $A$ is linear and strongly monotone, $B$ is nonlinear and Lipschitz, and $\tau > 0$ can be made small. Then $T$ is strongly monotone for small enough $\tau$.
Question. This is a "trick" from applied math. What is the name of this trick? It's "Lipschitz _______". Something like "Lipschitz Dominating", or "Lipschitz Mitigating" or something.
Brief Background. This trick arises when you discretize some nonlinear operator, and the resulting discrete operator (which is a matrix) can be split into a "good part", i.e. $A$, and a "bad part", i.e. $B$, where the time step is $\tau$. Then, because $A$ has properties that you want, the "bad behavior" of $B$ can be mitigated, provided you choose a small enough time step. For example, if $A$ is diagonally dominant, but $B$ isn't, you can make the matrix $A + \tau B$ diagonally dominant, provided $B$ is Lipschitz and $\tau$ is chosen small enough. Again, this is some well-known trick. I want to google it to learn more. But I don't know the name of the trick! So I'm just looking for a keyword to get me going!!