Iterated Functions Systems Composed of Generalized ι-Contractions.

The theory of iterated function systems (IFSs) has been an active area of research on fractals and various types of self-similarity in nature. The basic theoretical work on IFSs has been proposed by Hutchinson. In this paper, we introduce a new generalization of Hutchinson IFS, namely generalized q-contraction IFS, which is a finite collection of generalized q-contraction functions T1, . . ., TN from finite Cartesian product space X x ... x X into X, where (X, d) is a complete metric space. We prove the existence of attractor for this generalized IFS. We show that the Hutchinson operators for countable and multivalued q-contraction IFSs are Picard. Finally, when the map q is continuous, we show the relation between the code space and the attractor of q-contraction IFS. [ABSTRACT FROM AUTHOR]