APPROXIMATION ASPECTS OF SET-VALUED FRACTAL SURFACES

被引：0
|
作者：
Agrawal, Ekta [1 ]
Verma, Saurabh [1 ]
机构：
[1] IIIT Allahabad, Dept Appl Sci, Prayagraj 211015, India
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2025年
关键词：
Hausdorff metric; iterated function system; set-valued functions; Minkowski sum of sets; Bernstein polynomials;
D O I：
10.3934/dcdss.2025034
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The article deals with the construction of an alpha-fractal surface corresponding to a continuous compact set-valued function defined on a closed and bounded rectangular region of the Euclidean plane via an iterated function system. Additionally, the fractal function obtained follows a self-referential equation, exhibiting self-similarity in nature. Further, the condition is derived so that the fractal function is Ho<spacing diaeresis>lder continuous. In the end, Bernstein-type fractal approximations of a continuous convex compact set-valued function are elaborated, and bounds for approximation error are estimated.
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页数：21
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