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

Y. X. Cao, N. Liu and Y. S. Liang
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Y. X. Cao: Fundamental Education Department, Army Engineering University of PLA, Nanjing 211101, P. R. China
N. Liu: Fundamental Education Department, Army Engineering University of PLA, Nanjing 211101, P. R. China
Y. S. Liang: ��School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 01, 1-9

Abstract: 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.

Keywords: K-Dimension; Fractal Approximation; Fractal Remainder Term; Weierstrass Approximation Theorem (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500300

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