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A One-Dimensional Continuous Function With Unbounded Variation

Author

Listed:
  • 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)

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.

Suggested Citation

  • Dong Yang & Xia Yuan & Kang Zhang & Shiwei Wu & Chunxia Zhao, 2024. "A One-Dimensional Continuous Function With Unbounded Variation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-6.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:02:n:s0218348x24400073
    DOI: 10.1142/S0218348X24400073
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