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

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.