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On The Hewitt–Stromberg Dimension Of The Graphs Of Sums And Products Of Continuous Functions

Author

Listed:
  • RIM ACHOUR

    (Analysis, Probability and Fractals Laboratory LR18ES17, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Monastir 5000, Tunisia)

  • ZHIMING LI

    (��School of Mathematics, Northwest University Xi’an, Shaanxi 710127, P. R. China)

  • BILEL SELMI

    (Analysis, Probability and Fractals Laboratory LR18ES17, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Monastir 5000, Tunisia)

  • TINGTING WANG

    (��School of Mathematics, Northwest University Xi’an, Shaanxi 710127, P. R. China)

Abstract

In this paper, for a typical function Φ ∈𠒞(Y ) defined in an uncountable compact metric space Y, we give the lower Hewitt–Stromberg dimension of graphs GΦ(Y ) = {(y, Φ(y))|y ∈ Y } of the function Φ. Moreover, we investigate the decomposition of functions within 𠒞([0, 1]) based on the lower box dimension and the lower Hewitt–Stromberg dimension, revealing significant disparities compared to the context of the packing dimension. Second, we present some results on the lower Hewitt–Stromberg dimension of graphs of sums and products of continuous functions. The main proof is that for a given real number 1 ≤ β ≤ 2, some real-valued continuous functions in 𠒞([0, 1]) can be decomposed into the sum and product of two continuous real-valued functions, and the lower Hewitt–Stromberg dimension of the graph for each function is β.

Suggested Citation

  • Rim Achour & Zhiming Li & Bilel Selmi & Tingting Wang, 2025. "On The Hewitt–Stromberg Dimension Of The Graphs Of Sums And Products Of Continuous Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-16.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:01:n:s0218348x25500264
    DOI: 10.1142/S0218348X25500264
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