## 留言板

 引用本文: 李红达, 叶正麟, 高行山. 关于分形插值函数的连续性和可微性[J]. 应用数学和力学, 2002, 23(4): 422-428.
LI Hong-da, YE Zheng-lin, GAO Hang-shan. On the Continuity and Differentiability of a Kind of Fractal Interpolation Function[J]. Applied Mathematics and Mechanics, 2002, 23(4): 422-428.
 Citation: LI Hong-da, YE Zheng-lin, GAO Hang-shan. On the Continuity and Differentiability of a Kind of Fractal Interpolation Function[J]. Applied Mathematics and Mechanics, 2002, 23(4): 422-428.

## 关于分形插值函数的连续性和可微性

###### 作者简介:李红达(1966- ),男,陕西人,讲师,博士.
• 中图分类号: O174.1

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

• 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.
•  [1] Barnsley M F.Fractal functions and interpolation[J].Constr Approx,1986,2(3):303-329. [2] Barnsley M F.Fractal Everywhere[M].Boston:Academic Press,1988. [3] Massopust Peter R.Fractal function and applications[J].Chaos Solitons & Fractal,1997,8(2):171-190. [4] Peter Singer.Self-afine functions and wavelet series[J].J Math Appl,1999,240(2):518-551. [5] Jacques Levy-Vehel.Fractal approaches in signal processing[J].Fractals,1995,3(4):715-775. [6] Panagiotopoulos P D,Panagouli D.Mechanics on fractal bodies:Data compression using fractal[J].Chaos Solitons & Fractal,1997,8(2):253-267. [7] 谢和平,孙洪泉.分形插值曲面理论及应用[J].应用数学和力学,1998,19(4):297-306. [8] Bedford T.Helder expontents and box dimension for self-affine fractal function[J].Constr Approx,1989,5(1):33-48. [9] Donovan G,Geronimo J S,Massopust P R.Construction of orthogonal wavelets using fractal interpolation functions[J].SIAM J Math Anal,1996,27(4):1158-1192. [10] Barnsley M F,Harring A N.The calculus of interpolation function[J].J Approx Theory,1989,57(1):14-34.

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##### 出版历程
• 收稿日期:  2000-08-30
• 修回日期:  2001-12-21
• 刊出日期:  2002-04-15

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