| 一类非均匀分形插值函数的可微性 |
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| 引用本文： | 柯云泉.一类非均匀分形插值函数的可微性[J].数学杂志,2005,25(3):289-294. |
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| 作者姓名： | 柯云泉 |
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| 作者单位： | 绍兴文理学院数学系,浙江,绍兴,312000 |
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| 基金项目： | 浙江省重点扶植学科基金资助课题(1998494). |
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| 摘 要： | 本文研究一类分形插值函数的可微性问题，通过构造一迭代函数系，利用迭代函数系的唯一吸引子。给出了一类分形插值函数。并获得了此类分形插值函数在0，1]区间上几乎处处可微和在0，1]区间上某一点不可微判定的充分条件，推广了文献2]的结论。
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| 关 键 词： | 非等距插值点 迭代函数系 分形插值函数 可微性 |
| 文章编号： | 0255-7797(2005)03-0289-06 |
THE DIFFERENTIABILITY OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS |
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| KE Yun-Quan.THE DIFFERENTIABILITY OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS[J].Journal of Mathematics,2005,25(3):289-294. |
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| Authors: | KE Yun-Quan |
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| Abstract: | In this paper we investigate the differentiability of a class of fractal interpolation functions. Based on the unique attractor of iterated function system which is constructed, we give a class of fractal interpolation functions and obtain the sufficient conditions of almost everywhere differentiability on interval0,1] and non-differentiability at certain point on it. The results in paper 2] are extended. |
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| Keywords: | non-isometric interpolation point iterated function system fractal interpolation function differentiability |
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