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Non-stationary $\alpha$-fractal functions and their dimensions in various function spaces. (arXiv:2303.10206v1 [math.DS]) http://arxiv.org/abs/2303.10206

Non-stationary $α$-fractal functions and their dimensions in various function spaces

In this article, we study the novel concept of non-stationary iterated function systems (IFSs) introduced by Massopust in 2019. At first, using a sequence of different contractive operators, we construct non-stationary $α$-fractal functions on the space of all continuous functions. Next, we provide some elementary properties of the fractal operator associated with the nonstationary $α$-fractal functions. Further, we show that the proposed interpolant generalizes the existing stationary interpolant in the sense of IFS. For a class of functions defined on an interval, we derive conditions on the IFS parameters so that the corresponding non-stationary $α$-fractal functions are elements of some standard spaces like bounded variation space, convex Lipschitz space, and other function spaces. Finally, we discuss the dimensional analysis of the corresponding non-stationary $α$-fractal functions on these spaces.

arxiv.org
March 21, 2023 at 3:10 AM · · feed2toot · 0 · 0 · 0
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