| 分段线性函数及其应用研究 |
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| 引用本文： | 庄方敏,黄若婷,陈满春.分段线性函数及其应用研究[J].韩山师范学院学报,2013(6):20-24. |
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| 作者姓名： | 庄方敏 黄若婷 陈满春 |
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| 作者单位： | 韩山师范学院数学与应用数学系,广东潮州,521041 |
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| 基金项目： | 韩山师范学院大学生创新实验（实践）项目（项目编号：NO.2012-20）. |
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| 摘 要： | 分段线性连续函数是一类有着广泛应用的连续函数。本文首先证明：对任意的连续函数可用分段线性连续函数去一致逼近和一致收敛。其次，证明可把通过求分段线性连续函数的不动点来得到相应连续函数不动点的近似值。利用matlab程序，实现了在计算机上输出分段线性连续函数的所有不动点。最后，给出以上结论在经济学中的一个应用。
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| 关 键 词： | 分段线性连续函数 一致逼近 闭区间 连续函数 不动点 |
A Research on Piecewise Linear Function and Its Applications |
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| ZHUANG Fang-min,HUANG Ruo-ting,CHEN Man-chun.A Research on Piecewise Linear Function and Its Applications[J].Journal of Hanshan Teachers College,2013(6):20-24. |
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| Authors: | ZHUANG Fang-min HUANG Ruo-ting CHEN Man-chun |
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| Institution: | ZHUANG Fang-min, HUANG Ruo-ting, CHEN Man-chun |
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| Abstract: | Piecewise linear continuous function is a kind of continuous function which has a broad appli-cation. This paper firstly shows that any continuous function can be used uniformly approximated and uniform-ly convergent by piecewise linear continuous functions. Secondly, we can get an approximate value of a fixed point of a continuous map by seeking a fixed point of a corresponding piecewise linear continuous function. Moreover, we use the matlab program to output all fixed points of piecewise linear continuous functions on the computer. Finally,we give an application of the above conclusions in the economics. |
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| Keywords: | piecewise linear continuous function uniform approximation closed interval continu-ous function fixed point theorem |
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