Abstract
In this paper, we investigate the smoothness of non-equidistant fractal interpolation functions. We obtain the Holder exponents of such fractal interpolation functions by using the technique of operator approximation. At last, we discuss the series expressions of these functions and give a Box-counting dimension estimation of “critical” fractal interpolation functions by using our smoothness results.
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1991MR Subject Classification: 41A.
Supported by the National Natural Science Foundation of China
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Gang, C. The smoothness and dimension of fractal interpolation functions. Appl. Math. 11, 409–418 (1996). https://doi.org/10.1007/BF02662880
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DOI: https://doi.org/10.1007/BF02662880