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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| Format: | Article |
| Language: | English |
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MDPI AG
2024-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/22/3463 |
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| author | Anuj Kumar Salah Boulaaras Shubham Kumar Verma Mohamed Biomy |
| author_facet | Anuj Kumar Salah Boulaaras Shubham Kumar Verma Mohamed Biomy |
| author_sort | Anuj Kumar |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4f995ba8a43b430c97e8597e621312b3 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-4f995ba8a43b430c97e8597e621312b32024-11-26T18:11:30ZengMDPI AGMathematics2227-73902024-11-011222346310.3390/math12223463Non-Stationary Fractal Functions on the Sierpiński GasketAnuj Kumar0Salah Boulaaras1Shubham Kumar Verma2Mohamed Biomy3Department of Mathematics, Siddharth University Kapilvastu, Siddharthnagar 272202, IndiaDepartment of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi ArabiaCouncil of Finance and Mathematical Research, New Delhi 110016, IndiaDepartment of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi ArabiaFollowing 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.https://www.mdpi.com/2227-7390/12/22/3463Hausdorff dimensionself-SimilaritySierpiński gasketfractal functionHölder continuityfractional derivatives |
| spellingShingle | Anuj Kumar Salah Boulaaras Shubham Kumar Verma Mohamed Biomy Non-Stationary Fractal Functions on the Sierpiński Gasket Mathematics Hausdorff dimension self-Similarity Sierpiński gasket fractal function Hölder continuity fractional derivatives |
| title | Non-Stationary Fractal Functions on the Sierpiński Gasket |
| title_full | Non-Stationary Fractal Functions on the Sierpiński Gasket |
| title_fullStr | Non-Stationary Fractal Functions on the Sierpiński Gasket |
| title_full_unstemmed | Non-Stationary Fractal Functions on the Sierpiński Gasket |
| title_short | Non-Stationary Fractal Functions on the Sierpiński Gasket |
| title_sort | non stationary fractal functions on the sierpinski gasket |
| topic | Hausdorff dimension self-Similarity Sierpiński gasket fractal function Hölder continuity fractional derivatives |
| url | https://www.mdpi.com/2227-7390/12/22/3463 |
| work_keys_str_mv | AT anujkumar nonstationaryfractalfunctionsonthesierpinskigasket AT salahboulaaras nonstationaryfractalfunctionsonthesierpinskigasket AT shubhamkumarverma nonstationaryfractalfunctionsonthesierpinskigasket AT mohamedbiomy nonstationaryfractalfunctionsonthesierpinskigasket |