一类非线性分形插值函数

摘要

A kind of nonlinear iterated function system is constructed on the basis of the generation of thernfractal interpolation function. The iterated function system is studied, and its formation condition isrnverified. The existence and uniqueness of attractor for the iterated function system are proved, and arngraph of a fractal interpolation function just is the attractor. Finally, an example is given to illustrate thisrnproblem.%从分形插值函数的生成条件入手,构造了一类非线性迭代函数系.对这类非线性迭代函数系进行研究,验证了它的生成条件,并证明了它存在唯一的吸引子,并且迭代函数系的吸引子就是它所生成的分形插值函数的图像.最后,通过一个实例验证了本文结论.