Graphs of continuous functions and fractal dimensions

Manuj Verma and Amit Priyadarshi

Chaos, Solitons & Fractals, 2023, vol. 172, issue C

Abstract: In this paper, we show that, for any β∈[1,2], a given strictly positive (or strictly negative) real-valued continuous function on [0,1] whose graph has the upper box dimension less than or equal to β can be decomposed as a product of two real-valued continuous functions on [0,1] whose graphs have upper box dimensions equal to β. We also obtain a formula for the upper box dimension of every element of a ring of polynomials in a finite number of continuous functions on [0,1] over the field R.

Keywords: Box dimension; Graph of function; Continuous function (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004149

DOI: 10.1016/j.chaos.2023.113513

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