韩山师范学院学报
韓山師範學院學報
한산사범학원학보
JOURNAL OF HANSHAN TEACHERS COLLEGE
2013年
6期
20-24
,共5页
分段线性连续函数%一致逼近%闭区间%连续函数%不动点
分段線性連續函數%一緻逼近%閉區間%連續函數%不動點
분단선성련속함수%일치핍근%폐구간%련속함수%불동점
piecewise linear continuous function%uniform approximation%closed interval%continu-ous function%fixed point theorem
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。
分段線性連續函數是一類有著廣汎應用的連續函數。本文首先證明：對任意的連續函數可用分段線性連續函數去一緻逼近和一緻收斂。其次，證明可把通過求分段線性連續函數的不動點來得到相應連續函數不動點的近似值。利用matlab程序，實現瞭在計算機上輸齣分段線性連續函數的所有不動點。最後，給齣以上結論在經濟學中的一箇應用。
분단선성련속함수시일류유착엄범응용적련속함수。본문수선증명：대임의적련속함수가용분단선성련속함수거일치핍근화일치수렴。기차，증명가파통과구분단선성련속함수적불동점래득도상응련속함수불동점적근사치。이용matlab정서，실현료재계산궤상수출분단선성련속함수적소유불동점。최후，급출이상결론재경제학중적일개응용。
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.
