Phi-contractive parent-child infinite IFSs and orbital phi-contractive infinite IFSs

TL;DR

This paper introduces new classes of infinite iterated function systems, phi-contractive parent-child and orbital IIFS, and proves their fractal operators are weakly Picard, advancing the theoretical understanding of fractal constructions.

Contribution

It defines phi-contractive parent-child and orbital IIFS and establishes their fractal operators as weakly Picard, providing new insights into infinite fractal systems.

Findings

Fractal operator is weakly Picard for the new IIFS classes

Develops shift space and canonical projection concepts for these systems

Enhances theoretical framework of infinite fractal systems

Abstract

In this paper we introduce the notions of phi-contractive parent-child infinite iterated function system (pcIIFS) and orbital phi-contractive infinite iterated function system (oIIFS) and we prove that the corresponding fractal operator is weakly Picard. The corresponding notions of shift space, canonical projection and their properties are also treated.