Open Access
Research Article
The ϕ-Topological Conformal Dimension for the Sierpinski Carpet
*Anouar Ben MabroukCorresponding authoranouar.benmabrouk@fsm.rnu.tnDepartment of MathematicsFaculty of SciencesUniversity of TabukSaudi ArabiaView full profile → , Zied Douzidouzi.fsm@gmail.comDepartment of MathematicsFaculty of SciencesAnalysis, Probability & Fractals LaboratoryUniversity of MonastirMonastir, LR18ES17, 5000, TunisiaView full profile → , Bilel Selmibilel.selmi@isetgb.rnu.tnDepartment of MathematicsFaculty of SciencesAnalysis, Probability & Fractals LaboratoryUniversity of Monastir andMonastir, LR18ES17, 5000, TunisiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 22 Sep 2021
- Accepted:
- 31 Dec 2021
- Published Online:
- 15 Jun 2022
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- 1726037X.2022.2079264
- Pages:
- 33–53
Abstract
In this paper, a generalized fractal dimension is introduced based on a combination of the topological dimension, conformal dimension, and the ϕ-conformal dimension. Lower and upper bound estimates of the new variant of dimension are provided for the case of the Sierpinski carpet fractal set. Moreover, the equality of such bounds is proved for a large class of the basic measure ϕ.
Keywords
Subject Classifications
28A2028A7528A7828A8049Q15
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