A ONE-DIMENSIONAL CONTINUOUS FUNCTION WITH UNBOUNDED VARIATION

Dong Yang, Xia Yuan, Kang Zhang, Shiwei Wu and Chunxia Zhao
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Dong Yang: School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
Xia Yuan: School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
Kang Zhang: School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
Shiwei Wu: School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
Chunxia Zhao: School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 02, 1-6

Abstract: In this paper, we consider a function with only one unbounded variation point and study the box dimension of its graph. We prove that the function is continuous and differentiable on a certain interval. Moreover, we show that the function is of unbounded variation on the domain of definition. Using our techniques, we also estimate the box dimension of the graph of the function.

Keywords: Fractal Function; Unbounded Variation; Box Dimension (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24400073

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