关于分形插值函数的连续性和可微性

基金项目: 国家自然科学基金资助项目(10071060)

On the Continuity and Differentiability of a Kind of Fractal Interpolation Function

1.
State Key Laboratry of Information, Security Graduate School, Chinese Academy of Sciences, Beijing 100039, P. R. China;
2.
Department of Mathematics and Information, Northwestern Polytechnical University, Xi'an 710072, P. R. China;
3.
Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, P. R. China

摘要: 获得了由迭代函数系统(IFS)定义的两类分形插值函数具有Hlder连续性的充分条件,给出了这两类分形插值函数连续可微的充要条件,并证明了可微分形插值函数的导函数是由关联IFS生成的分形插值函数.
- 分形 /
- 插值函数 /
- Hlder连续 /
- 可微性
Abstract: The sufficient conditions of Helder continuity of two kinds of fractal interpolation functions defined by IFS were obtained. The sufficient and necessary condition for its differentiability was proved. Its derivative was a fractal interpolation function generated by the associated IFS, if it is differentiable.
- fractal /
- interpolation function /
- Helder continuity /
- differentiability

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