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.

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In present times, there has been a substantial endeavor to generalize the classical notion of iterated function system (IFS). We introduce a new type of non-linear contraction namely cyclic Meir-Keeler contraction, which is more generic than the famous Banach contraction. We show the perseverance and uniqueness of the fixed point for the cyclic Meir-Keeler contraction. Using this result, we propose the cyclic Meir-Keeler IFS in the literature for construction of fractals. Furthermore, we extend the theory of countable IFS and generalized IFS by using these cyclic Meir-Keeler contraction maps.

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