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.%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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