Cyclic generalized iterated function systems

Abstract

In this article, we introduce the notion of cyclic generalized iterated function system (GIFS), which is a family of functions f1,f2,…,fM:Xk→X, where each fi is a cyclic generalized φ‐contraction (contractive) map on a collection of subsets {Bj}j=1p of a complete metric space (X,d) respectively, and k,M,p are natural numbers. When Bj,j=1,2,…,p are closed subsets of X, we show the existence of attractor of this cyclic GIFS, and investigate its properties. Further, we extend our ideas to cyclic countable GIFS.

The Generalized Iterated Function System and Common Attractors of Generalized Hutchinson Operators in Dislocated Metric Spaces

“…Sv < r 2 (x, y 2 ) + h 2 (x, y 2 , v(ω(x, y 2 ))), (13) it holds that Tu ≤ r 2 (x, y 2 ) + h 1 (x, y 2 , u(ω(x, y 2 ))) + λ, (…”

“…Recently, some useful results appeared in [8][9][10][11][12]. Pasupathi et al [13] developed new iterated function systems consisting of cyclic contractions and discussed some special properties of the Hutchinson operator associated with cyclic iterated function systems. Recently, Thangaraj and Easwaramoorthy [14] obtained some interesting results and consequences of the controlled Fisher iterated function system and controlled Fisher fractals.…”

“…It is also demonstrated with the idea of constructing a new type of fractals that are common attractors generated by generalized iterated function system. It is believed that the proposed research work of common attractors with generalized rational contractive operators can be established for deriving fractals through admissible hybrid contractions [19] and generalized cyclic contractions [13] maps. The proposed theory will also lead to a new path for developing new kind of fractals and their consequences based on generalized contractions in the extraction of dislocated metric spaces.…”

Fractals via Controlled Fisher Iterated Function System

“…The authors developed the notion of a topological IFS attractor in the reference, which generalizes the familiar IFS attractor. Every IFS attractor is also a topological IFS attractor, but the reverse is not true [39][40][41].…”