Abstract

In this article, we manifest the existence of a new class of \(\alpha \) -fractal functions without endpoint conditions in the space of continuous functions. Furthermore, we add the existence of the same class in numerous spaces such as the Hölder space, the convex Lipschitz space, and the oscillation space. We also estimate the fractal dimensions of the graphs of the newly constructed \(\alpha \) -fractal functions adopting some function spaces and covering methods.

中文翻译：

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$$\alpha $$ 的分形维数 - 无端点条件的分形函数

摘要

在本文中，我们证明了连续函数空间中不存在端点条件的一类新的\(\alpha \)分形函数的存在。此外，我们还添加了同一类在许多空间中的存在性，例如霍尔德空间、凸利普希茨空间和振荡空间。我们还采用一些函数空间和覆盖方法来估计新构造的\(\alpha \) -分形函数图的分形维数。