ON THE HEWITT–STROMBERG DIMENSION OF THE GRAPHS OF SUMS AND PRODUCTS OF CONTINUOUS FUNCTIONS

Rim Achour (), Zhiming Li, Bilel Selmi () and Tingting Wang ()
Additional contact information
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

FRACTALS (fractals), 2025, vol. 33, issue 01, 1-16

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.

Keywords: Box-Dimensions; Hausdorff and Packing Measures; Graph of Function; Continuous Function; Decompositions (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X25500264
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:33:y:2025:i:01:n:s0218348x25500264

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X25500264

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().