Attractors of fiber φ -type iterated function systems and canonical projection

In this paper, we have investigated attractors of fiber φ-type iterated function systems and their connection to canonical projections. Building on the foundations of Hutchinson-Barnsley theory, which explores fractal generation via contraction mappings in metric spaces, the study extends the concept of iterated function system to a generalized fiber φ-type iterated function system using (c)-comparison functions. The analysis demonstrates the existence of unique attractors and establishes the conditions under which these systems admit canonical projections.