Hausdorff–Besicovitch dimension of the graph of one continuous nowhere-differentiable function

• Date: 2009
• Main Authors: O., B. Panasenko, Панасенко, O. Б.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3094
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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} &...