In this paper, we have done some research studies on the fractal dimension of the sum of two continuous functions with different $K$-dimensions and approximation of $s$-dimensional fractal functions. We first investigate the $K$-dimension of the linear combination of fractal function whose $K$-dimension is $s$ and the function satisfying Lipschitz condition is still $s$-dimensional. Then, based on the research of fractal term and the Weierstrass approximation theorem, an approximation of the $s$-dimensional continuous function is given, which is composed of finite triangular series and partial Weierstrass function. In addition, some preliminary results on the approximation of one-dimensional and two-dimensional fractal continuous functions have been given.

在本文中，我们对两个不同连续函数之和的分形维数进行了一些研究。$K$-尺寸和近似值$s$维分形函数。我们首先调查$K$- 分形函数线性组合的维数，其$K$- 维度是$s$满足 Lipschitz 条件的函数仍然是$s$-维度。然后，基于分形项和Weierstrass近似定理的研究，近似$s$给出了由有限三角级数和偏Weierstrass函数组成的维连续函数。此外，还给出了一维和二维分形连续函数逼近的一些初步结果。