论文标题
设置值α-骨骼函数
Set-valued α-fractal functions
论文作者
论文摘要
在本文中，我们介绍了$α$ fractal函数的概念和分形近似的概念，该概述是在实数的封闭且有界的间隔下定义的设置值连续图。另外，我们研究了这种分形功能的一些特性。此外，我们估计给定的连续函数与其$α$ - 分类函数之间的扰动误差。此外，我们定义了与文献中介绍的标准图不同的设置值函数的新图，并在一些特殊类别值值函数的新定义图的分形维度上建立了一些界限。另外，我们解释了用示例定义这个新图的必要性。在续集中，我们证明了$α$ fractal函数的新图是迭代功能系统的吸引子。
In this paper, we introduce the concept of the $α$-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers. Also, we study some properties of such fractal functions. Further, we estimate the perturbation error between the given continuous function and its $α$-fractal function. Additionally, we define a new graph of a set-valued function different from the standard graph introduced in the literature and establish some bounds on the fractal dimension of the newly defined graph of some special classes of set-valued functions. Also, we explain the need to define this new graph with examples. In the sequel, we prove that this new graph of an $α$-fractal function is an attractor of an iterated function system.
