  We introduce generalised triple homomorphism between Jordan Banach triple
systems as a concept which extends the notion of generalised homomorphism
between Banach algebras given by Jarosz and Johnson in 1985 and 1987,
respectively. We prove that every generalised triple homomorphism between
JB$^*$-triples is automatically continuous. When particularised to
C$^*$-algebras, we rediscover one of the main theorems established by Johnson.
We shall also consider generalised triple derivations from a Jordan Banach
triple $E$ into a Jordan Banach triple $E$-module, proving that every
generalised triple derivation from a JB$^*$-triple $E$ into $E^*$ is
automatically continuous.
