  In 2016, Hou and Wang introduced the concept of multiple mappings based on
iterated function system, which is an important branch of fractal theory. In
this paper, we introduce the definitions of shadowing, average shadowing,
transitive, weakly mixing, mixing, chain transitive and chain mixing properties
of multiple mappings from a set-valued perspective. We show that both two
continuous self-maps have shadowing (respectively, average shadowing,
transitive, weakly mixing, mixing) property may not imply the multiple mappings
they form has the corresponding property. While a sufficient condition for
multiple mappings to be transitive (respective, weakly mixing, mixing, chain
transitive, chain mixing) is given. Both shadowing and average shadowing
properties are invariant under the iterative action of multiple mappings. Also,
we study that for multiple mappings shadowing property plus chain mixing
implies mixing and average shadowing properties implies chain transitivity.
