中文摘要：

迭代函数系（iterated function system，IFS）是产生分形的一种非常有用的方法．一个IFS通常是由完备度量空间上的一组压缩映射构成，它的吸引子一般是分形．在经典的Kannan映射和广义K映射的基础上，引入了一类广义K迭代函数系（K—IFS）．证明了这类广义K—IFS存在唯一的吸引子，给出了广义K—IFS的吸引子的拼贴定理，构造了一个用广义K—IFS的吸引子逼近给定紧集的例子．

英文摘要：

Iterated function systems （IFSs） have been proven to be a very useful way of producing self-similar or fractal objects. An IFS is usually a finite collection of contractive mappings of a complete metric space into itself, and its attractor is generally a fractal set. Based on the classical Kannan mapping and generalized K mapping, a class of generalized K-IFSs was introduced. The existence and uniqueness of the attractor for the generalized K-IFS consisting of the generalized K-mappings were proved by means of the fixed point theorem for the generalized K-mappings. In addition, the collage theorem for the class of generalized K-IFSs was given, and an example of using the attractor of generalized K-IFS to approximate a given compact set was constructed.