This paper contains a review of results concerning “generalized”
attractors for a large class of iterated function systems
$\{w_{i}:i\in I\}$ acting on a complete separable metric space.
This generalization, which originates in the Banach contraction
principle, allows us to consider a new class of sets, which we
call semi-attractors (or semifractals). These sets have many
interesting properties. Moreover, we give some fixed-point
results for Markov operators acting on the space of Borel
measures, and we show some relations between semi-attractors and
supports of invariant measures for such Markov operators.
Finally, we also show some relations between multifunctions and
transition functions appearing in the theory of Markov operators.