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 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.