Non-Stationary Fractal Functions on the Sierpiński Gasket

Anuj Kumar, Salah Boulaaras (), Shubham Kumar Verma and Mohamed Biomy
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Anuj Kumar: Department of Mathematics, Siddharth University Kapilvastu, Siddharthnagar 272202, India
Salah Boulaaras: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Shubham Kumar Verma: Council of Finance and Mathematical Research, New Delhi 110016, India
Mohamed Biomy: Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia

Mathematics, 2024, vol. 12, issue 22, 1-11

Abstract: Following the work on non-stationary fractal interpolation ( Mathematics 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.

Keywords: Hausdorff dimension; self-Similarity; Sierpi?ski gasket; fractal function; Hölder continuity; fractional derivatives (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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