In this paper, we consider some generalization of the Banach contraction principle, namely cyclic contraction and cyclic \(\varphi \)-contraction. For the application to the fractal, we develop new iterated function systems (IFS) consisting of cyclic contractions and cyclic \(\varphi \)-contractions. Further, we discuss about some special properties of the Hutchinson operator associated with the cyclic (c)-comparison IFS.

中文翻译：

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循环迭代功能系统

在本文中，我们考虑了Banach收缩原理的一些概括，即循环收缩和循环\（\ varphi \）-收缩。对于分形的应用，我们开发了由循环收缩和循环\（\ varphi \）-收缩组成的新的迭代函数系统（IFS）。此外，我们讨论了与循环（c）比较IFS相关的Hutchinson算子的一些特殊性质。