We investigate some properties of approximately quasi inner generalized dynamics and quasi approximately inner generalized derivations on modules. In particular, we prove that if A is a C*-algebra, is the generator of a generalized dynamics on an A-bimodule M satisfying and there exist two sequences of self adjoint elements in A such that for all in a core for , , then is approx...

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.