The main result of this paper states that for a given countable system of data \(\varDelta \), there exists a countable iterated function system consisting of Rakotch contractions, such that its attractor is the graph of a fractal interpolation function corresponding to \(\varDelta \). In this way, on the one hand, we generalize a result due to Secelean (see Univ Beograd Publ Elektrotehn Fak Ser Mat 14:11–19, 2003) by considering countable systems consisting of Rakotch contractions rather than Banach contractions. On the other hand, we generalize a result due to Ri (see Indag Math 29:962–971, 2018) by considering countable (rather than finite) systems consisting of Rakotch contractions. Some exemplifications are provided.

本文的主要结果表明，对于给定的可数数据系统\(\varDelta \)，存在一个由 Rakotch 收缩组成的可数迭代函数系统，使得它的吸引子是对应于\( \varDelta \)。这样，一方面，我们通过考虑由 Rakotch 收缩而不是 Banach 收缩组成的可数系统来概括由于 Secelean（参见 Univ Beograd Publ Elektrotehn Fak Ser Mat 14:11-19, 2003）的结果。另一方面，我们通过考虑由 Rakotch 收缩组成的可数（而不是有限）系统来概括由 Ri（参见 Indag Math 29:962–971, 2018）得出的结果。提供了一些示例。