arXiv:2211.14661v1 [math.PR] 26 Nov 2022 Page 1 Iterated Function Systems: A
Comprehensive Survey Ramen Ghosh ∗ Jakub Mareček † November 29, 2022 Abstract We …

We give a systematic account of iterated function systems (IFS) of weak contractions of
different types (Browder, Rakotch, topological). We show that the existence of attractors and …

In this paper, we consider some generalization of the Banach contraction principle, namely
cyclic contraction and cyclic φ φ-contraction. For the application to the fractal, we develop …

The theory of iterated function systems (IFS) and of infinite iterated function systems
consisting of contraction mappings has been studied in the last decades. Some extensions …

We introduce the notion of a generalized iterated function system (GIFS), which is a finite
family of functions, where is a metric space and. In case that is a compact metric space and …

In the last decades there has been a current effort to extend the classical Hutchinson theory
of iterated function systems composed by contractions on a metric space X into itself to more …

Multivalued fractals are considered as fixed-points of certain induced union operators, called
the Hutchinson–Barnsley operators, in hyperspaces of compact subsets of the original …

The theory of iterated function systems (IFSs) has been an active area of research on fractals
and various types of self-similarity in nature. The basic theoretical work on IFSs has been …

In this paper we prove a generalization of Istr\u {a}\c {t} escu's theorem for convex
contractions. More precisely, we introduce the concept of iterated function system consisting …

A new class of fractals called hyperfractals is systematically investigated. Their underlying
fractals in supporting spaces are multivalued fractals developed by ourselves in our earlier …