A well-known theorem of fractal geometry, presented by J. Hutchinson ([16]),
says that there exists a unique compact self similar set with respect to any
finite set of contractions on a complete metric space. Motivated by this
result, in this paper, we prove fixed set theoretical theorems in order to
obtain useful variations of this important result for Meir-Keeler operators
and using the technique of measure of weak-noncompactness for operators
acting in Banach spaces and Banach algebras.