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

Anarul Islam Mondal; Sangita Jha

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arXiv · 2303.10206

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

Anarul Islam Mondal·Sangita Jha

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Abstract

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 $\alpha$-fractal functions on the space of all continuous functions. Next, we provide some elementary properties of the fractal operator associated with the nonstationary $\alpha$-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 $\alpha$-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 $\alpha$-fractal functions on these spaces.

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Anarul Islam Mondal, Sangita Jha. 2023-03-17. Non-stationary $\alpha$-fractal functions and their dimensions in various function spaces. https://arxiv.org/abs/2303.10206

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