Let , be Hilbert modules over -algebras , , respectively, and let be a map. We say that is a -morphism if
Using a fixed point approach the authors prove stability results for -morphisms under the assumption of the form
where is a “control” function satisfying some technical conditions. In particular, for (with some and ), there exists a unique -morphism such that
If both inequalites (in the assumption and in the assertion) are postulated for .