Fixed Point Theorems of the Iterated Function Systems

Abstract

In this paper, we present some fixed point theorems of iterated function systems consisting of $α$-$ψ$-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of generalized metric space, which is also extensively applied in topological dynamic system.