  We derive integrable equations starting from autonomous mappings with a
general form inspired by the multiplicative systems associated to the affine
Weyl group E$_8^{(1)}$. Five such systems are obtained, three of which turn out
to be linearisable and the remaining two are integrable in terms of elliptic
functions. In the case of the linearisable mappings we derive nonautonomous
forms which contain a free function of the dependent variable and we present
the linearisation in each case. The two remaining systems are deautonomised to
new discrete Painlev\'e equations. We show that these equations are in fact
special forms of much richer systems associated to the affine Weyl groups
E$_7^{(1)}$ and E$_8^{(1)}$ respectively.
