Dimensional analysis of \(\alpha\)-fractal functions. (English) Zbl 1478.28009
Summary: We provide a rigorous study on dimensions of fractal interpolation functions defined on a closed and bounded interval of \(\mathbb{R}\) which are associated to a continuous function with respect to a base function, scaling functions and a partition of the interval. In particular, we calculate an exact estimation of box dimension of \(\alpha\)-fractal functions under suitable hypotheses on the iterated function system.
Keywords:
iterated function systems; fractal interpolation functions; Hausdorff dimension; box dimension; open set conditionReferences:
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