Exploring Iterated Implicit Function Systems: Existence and Properties of Attractors

This paper investigates a type of iterated implicit function systems composed of equations Formula: see text, where Formula: see text is a continuous function, and Formula: see text is a constant. The existence of attractors of iterated implicit function systems is proved based on different equation conditions, including the equation Formula: see text containing the implicit function or being Formula: see text-contractive about Formula: see text. Meanwhile, we give definitions of implicit convergence of functions and monotone sequence of iterated implicit function systems. Finally, some properties of attractors of iterated implicit function systems are elucidated.