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\({\mathcal {L}}^p\)-Approximation Using Fractal Functions on the Sierpiński Gasket

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We are concerned with the approximation of functions by fractal functions with respect to \({\mathcal {L}}^p\)-norm on the Sierpiński gasket. We define the \(\alpha \)-fractal function in \({\mathcal {L}}^p\) space. The properties such as topological isomorphism and many others, which are closely associated with the fractal operator will be discussed in more detail. We also prove the existence of a non-trivial closed invariant subspace for the fractal operator. Additionally, we define set-valued mapping and discuss some useful properties.

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  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India

    Vishal Agrawal & Tanmoy Som

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  1. Vishal Agrawal
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  2. Tanmoy Som
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Agrawal, V., Som, T. \({\mathcal {L}}^p\)-Approximation Using Fractal Functions on the Sierpiński Gasket. Results Math 77, 74 (2022). https://doi.org/10.1007/s00025-021-01565-5

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