  The average shadowing property is considered for set-valued dynamical
systems, generated by parameterized IFS, which are uniformly contracting, or
conjugacy, or products of such ones. We also prove that if a continuous
surjective IFS F on a compact metric space X has the aver- age shadowing
property, then every point x is chain recurrent. Moreover, we introduce some
examples and investigate the relationship between the original shadowing
property and shadowing property for IFS. For example, this is proved that the
Sierpinski IFS has the average shadowing property. Then we shows that there is
an IFS F on S1 such that F does not sat- isfy the average shadowing property
but every point x in S1 is a chain recurrent.
