This note aims to extend the notion of affine zipper fractal interpolation function from the case of a finite data set to an infinite sequence of data points. We work with a slightly more general setting wherein the assumption of affinity on the functions involved in the construction of the zipper fractal interpolant is dropped. Invoking the iterative functional equation for the countable zipper fractal interpolant, its stability with a perturbation of data points and sensitivity to perturbations in the maps that define the zipper are examined. In the second part of this note, the countable zipper fractal interpolation is used to obtain a parameterized family of zipper fractal functions corresponding to a prescribed real-valued Lipschitz continuous function on a closed bounded interval in \(\mathbb {R}\). An operator obtained by associating each Lipschitz continuous function to its fractal counterpart is approached from the standpoint of nonlinear functional analysis and perturbation theory of operators.

本文旨在将仿射拉链分形插值函数的概念从有限数据集扩展到无限个数据点序列。我们使用稍微更一般的设置进行工作，其中放弃了对拉链分形内插的构造中涉及的函数的亲和力假设。调用可数拉链分形插值的迭代函数方程，检查其在数据点扰动下的稳定性以及在定义拉链的映射中对扰动的敏感性。在本说明的第二部分中，可计数的拉链分形插值用于获得与\（\ mathbb {R} \）中的封闭有界区间上的指定实值Lipschitz连续函数相对应的参数化拉链分形函数族。。从非线性功能分析和算子微扰理论的角度出发，研究了通过将每个Lipschitz连续函数与其分形对应物相关联而获得的算子。