中文摘要：

基于Barnsley的分形构造法，构造了一类具有双参数的非线性迭代函数系．与传统的线性迭代函数系相比，所构造的迭代函数系具有更高的灵活性，它的吸引子即分形插值曲线能更好地拟合实验数据．证明了这类分形插值函数关于双参数是Lipschitz连续的，并讨论了这类分形插值曲线的参数界定问题，最后给出了关于双参数的充分条件．为图象压缩和数据拟合等实际应用提供了理论基础．

英文摘要：

Based on the fractal constructive methods of Barnsley,a class of nonlinear iterated function systems with two parameters was constructed. Compared to the traditional linear iterated function system,the constructed iterated function systems have more flexibility. Their attractors, fractal interpolation curves, could be used to fit experimental data more effectively. It was shown that such fractal interpolation functions were Lipschitz continuous with respect to two parameters. The parameter identification problem of these fractal interpolation curves was investigated,and a sufficient condition that two parameters must obey was presented. The resuits of the present work may provides theoretical foundation for the applications of image compression and data fitting.