| 一类广义康托函数的构造及其解析式 |
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| 引用本文： | 沈兴灿.一类广义康托函数的构造及其解析式[J].纺织高校基础科学学报,2008,21(3):284-288. |
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| 作者姓名： | 沈兴灿 |
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| 作者单位： | 陕西师范大学,数学与信息科学学院,陕西,西安,710062 |
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| 摘 要： | 利用齐次康托集F{mi}构造一类广义康托函数φ（x）.应用实数的康托展式讨论广义康托函数φ（x）在齐次康托集F{mi}构成区间的特征,从而得到了广义康托函数φ（x）的解析式.推广了三分康托函数,获得一类新的分形曲线.
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| 关 键 词： | 康托集 康托函数 康托展式 |
The construction of a class of general Cantor function and the analytic representation |
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| SHEN Xing-can.The construction of a class of general Cantor function and the analytic representation[J].Basic Sciences Journal of Textile Universities,2008,21(3):284-288. |
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| Authors: | SHEN Xing-can |
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| Affiliation: | SHEN Xing-can (College of Mathematics and Information Science, Shaanxi Normal University, Xi＇an 710062, China) |
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| Abstract: | A class of general Cantor function φ（x） was constructed with the homogeneous Cantor set F{mi}, and the characterization of function φ（x） in the homogeneous Car, tor set F{mi} was investgated by applying the Cantor expansions of real numbers. As a result,the analytic representation of function φ（x） is obtained. Ternary Cantor function is generalized and a class new fractal curve is constructed. |
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| Keywords: | Cantor set Cantor function Cantor expansion |
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