Analysis of α-fractal functions without boundary point conditions on the Sierpiński gasket

Gurubachan,, V.V.M.S. Chandramouli and S. Verma

Applied Mathematics and Computation, 2025, vol. 486, issue C

Abstract: This note aims to manifest the existence of a class of α-fractal interpolation functions (α-FIFs) without boundary point conditions at the m-th level in the space consisting of continuous functions on the Sierpiński gasket (SG). Furthermore, we add the existence of the same class in the Lp space and energy space on SG. Under certain hypotheses, we show the existence of α-FIFs without boundary point conditions in the Hölder space and oscillation space on SG, and also calculate the fractal dimensions of their graphs.

Keywords: Sierpiński gasket; α-fractal interpolation function; Hausdorff dimension; Box dimension; Lp space; Energy space; Hölder space; Oscillation space (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:486:y:2025:i:c:s0096300324005332

DOI: 10.1016/j.amc.2024.129072

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