Let be a unital -algebra and be the positive part of the unit ball of . Let be a quasi-normed -module with quasi-norm and be a -Banach -module with -norm (i.e. and for ). The authors prove the Hyers-Ulam-Rassias stability of linear mappings from to , associated to the Cauchy functional equation and a generalized version of the Jensen equation. In the first case they assume that a function fulfils
for and for all from the unitary group if , and for all if . In the second case they assume that and for some integer we have
for and for all from the unit sphere of . In both cases the authors show that there is a unique -linear mapping satisfying
with certain stability constants which always tend to zero as .