Abstract
Fractal interpolation functions that produce smooth and non-smooth approximants constitute an advancement to various classical nonrecursive methods of approximation. However, in fractal approximation, the emphasis so far has been on the investigation of continuous functions interpolating prescribed data sets. In this article, we exclude the two properties – continuity and interpolation – inherent in fractal interpolation, and introduce the concept of fractal histopolation. That is, we study the area-matching properties of fractal functions that are integrable but not necessarily continuous.
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