Exploring Iterated Implicit Function Systems: Existence and Properties of Attractors

Abstract

This paper investigates a type of iterated implicit function systems composed of equations $F_n(x,y)=c$, where $F_n(x,y)$ is a continuous function, and $c$ is a constant. The existence of attractors of iterated implicit function systems is proved based on different equation conditions, including the equation $F_n(x,y)=c$ containing the implicit function or being ${\alpha }_n$-contractive about $y$. 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.