Non-Stationary Fractal Functions on the Sierpiński Gasket

Non-Stationary Fractal Functions on the Sierpiński Gasket

Following the work on non-stationary fractal interpolation (<i>Mathematics</i> 7, 666 (2019)), we study non-stationary or statistically self-similar fractal interpolation on the Sierpiński gasket (SG). This article provides an upper bound of box dimension of the proposed interpolants in...

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Bibliographic Details
Main Authors: Anuj Kumar, Salah Boulaaras, Shubham Kumar Verma, Mohamed Biomy
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Mathematics
Subjects:
Hausdorff dimension
self-Similarity
Sierpiński gasket
fractal function
Hölder continuity
fractional derivatives
Online Access:https://www.mdpi.com/2227-7390/12/22/3463
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Summary:Following the work on non-stationary fractal interpolation (<i>Mathematics</i> 7, 666 (2019)), we study non-stationary or statistically self-similar fractal interpolation on the Sierpiński gasket (SG). This article provides an upper bound of box dimension of the proposed interpolants in certain spaces under suitable assumption on the corresponding Iterated Function System. Along the way, we also prove that the proposed non-stationary fractal interpolation functions have finite energy.
ISSN:2227-7390

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