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arXiv · 2207.02635

Set-valued \alpha-fractal functions

Megha Pandey·Tanmoy Som·Saurabh Verma
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Abstract

In this paper, we introduce the concept of the $\alpha$-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 $\alpha$-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 $\alpha$-fractal function is an attractor of an iterated function system.

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Megha Pandey, Tanmoy Som, Saurabh Verma. 2022-07-06. Set-valued \alpha-fractal functions. https://arxiv.org/abs/2207.02635

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