Cyclic generalized iterated function systems. Issue 6 (5th December 2021) - Pasupathi, Rajan; Chand, Arya Kumar Bedabrata; Navascués, María Antonia; Sebastián, María Victoria
Abstract: In this article, we introduce the notion of cyclic generalized iterated function system (GIFS), which is a family of functions f 1, f 2, …, f M : X k → X, where each f i is a cyclic generalized φ ‐contraction (contractive) map on a collection of subsets { B j } j = 1 p of a complete metric space ( X, d ) respectively, and k, M, p are natural numbers. When B j, 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.