Fractal Dimension of $$\alpha $$ -Fractal Functions Without Endpoint Conditions

IF 1.1 3区数学 Q1 MATHEMATICS

Mediterranean Journal of Mathematics Pub Date : 2024-03-18 DOI:10.1007/s00009-024-02610-7

引用次数: 0

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.

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$$\alpha $$ 的分形维度 - 无端点条件的分形函数

摘要在本文中，我们证明了在连续函数空间中存在一类不带端点条件的新的$\alpha $-分形函数。此外，我们还补充了同一类函数在众多空间中的存在性，如荷尔德空间、凸立普茨空间和振荡空间。我们还采用一些函数空间和覆盖方法估计了新构造的 $α $ -分形函数的图的分形维数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mediterranean Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

261

审稿时长

6-12 weeks

期刊介绍： The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003. The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience. In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.