Hausdorff–Besicovitch dimension of the graph of one continuous nowhere-differentiable function
We investigate fractal properties of the graph of the function $$y = f(x) = ∑^{∞}_{k−1}\frac{β_k}{2^k} ≡ Δ^2_{β_1β_2…β_k…},$$ where $$\beta_1 = \begin{cases} 0 & \mbox{if } \alpha_1(x) = 0,\\ 1 & \mbox{if } \alpha_1(x) \neq 0,\\ \end{cases}$$ $$\beta_k = \begin{cases} β_{k−1} &...
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| Date: | 2009 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2009
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3094 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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