RESEARCH ON THE K-DIMENSION OF THE SUM OF TWO CONTINUOUS FUNCTIONS AND ITS APPLICATION

Abstract

In this paper, we have done some research studies on the fractal dimension of the sum of two continuous functions with different [Formula: see text]-dimensions and approximation of [Formula: see text]-dimensional fractal functions. We first investigate the [Formula: see text]-dimension of the linear combination of fractal function whose [Formula: see text]-dimension is [Formula: see text] and the function satisfying Lipschitz condition is still [Formula: see text]-dimensional. Then, based on the research of fractal term and the Weierstrass approximation theorem, an approximation of the [Formula: see text]-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.