论文标题
关于$ n $ atiterated功能系统与应用程序的序列的收敛
On the convergence of sequences in the space of $n$-iterated function systems with applications
论文作者
论文摘要
本文讨论了迭代函数系统序列的收敛概念。迭代功能系统的技术是构造具有分形性质的对象的几种方法之一，使用此方法获得的分形大多是自相似的。分形理论的进步发现了在物理科学，计算机科学和经济学领域的潜在应用。本文通过在由$ n $收缩功能组成的完整度量空间上引入所有迭代函数系统集中的度量功能，从而考虑了$ n $迭代功能系统的度量空间。此外，讨论了$ n $ - 迭代功能系统的序列，最终减少，库奇和收敛性。获得$ n $的序列的一些结果 - 迭代功能系统和收缩序列。文章中讨论的理论的实际用法将在最后探讨。
This article discusses the notion of convergence of sequences of iterated function systems. The technique of iterated function systems is one of the several methods to construct objects with fractal nature, and the fractals obtained with this method are mostly self-similar. The progress in the theory of fractals has found potential applications in the fields of physical science, computer science, and economics in abundance. This paper considers the metric space of $n$- iterated function systems by introducing a metric function on the set of all iterated function systems on a complete metric space consisting of $n$ contraction functions. Further, sequences of $n$- iterated function systems with decreasing, eventually decreasing, Cauchy and convergent properties are discussed. Some results on sequences of $n$- iterated function systems and sequences of contractions are obtained. The practical usage of the theory discussed in the article is explored towards the end.
