In this paper we present a method to generate new fractal interpolation curves. We ensure that attractors of nonlinear iterated function systems (IFSs) constructed by Geraghty contractions are graphs of some continuous functions which interpolate the given data. In particular, we give an explicit illustrative example to demonstrate the effectiveness of obtained results. Concerning IFSs, our methods and results extend known results from the literature.

中文翻译：

---

具有函数垂直比例因子的非线性分形插值曲线

在本文中，我们提出了一种生成新的分形插值曲线的方法。我们确保由格拉格蒂收缩构造的非线性迭代函数系统（IFS）的吸引子是内插给定数据的某些连续函数的图。特别是，我们给出一个明确的说明性示例，以证明所获得结果的有效性。关于IFS，我们的方法和结果扩展了文献中的已知结果。