Abstract

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 a generalization of the famous Banach contraction. We show the existence 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.

中文翻译：

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循环 Meir-Keeler 收缩及其分形

摘要

目前，人们已经做出了大量努力来概括迭代函数系统 (IFS) 的经典概念。我们引入了一种新型的非线性收缩，即循环 Meir-Keeler 收缩，它是著名的 Banach 收缩的推广。我们展示了循环 Meir-Keeler 收缩不动点的存在性和唯一性。使用这个结果，我们在文献中提出了用于构建分形的循环 Meir-Keeler IFS。此外，我们通过使用这些循环 Meir-Keeler 收缩图扩展了可数 IFS 和广义 IFS 的理论。