ON FRACTAL DIMENSIONS OF FRACTAL FUNCTIONS USING FUNCTION SPACES

被引：23
|
作者：
Chandra, Subhash [1 ]
Bbas, Syed A. [1 ]
机构：
[1] Indian Inst Technol Mandi, Sch Basic Sci, Kamand 175005, Himachal Prades, India
来源：
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2022年 / 106卷 / 03期
关键词：
fractal interpolation functions; convex-Lipschitz space; oscillation space; Hausdorff dimension; box dimension; HAUSDORFF DIMENSION; BOX DIMENSION; GRAPHS;
D O I：
10.1017/S0004972722000685
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Based on the work of Mauldin and Williams ['On the Hausdorff dimension of some graphs', Trans. Amer. Math. Soc. 298(2) (1986), 793-803] on convex Lipschitz functions, we prove that fractal interpolation functions belong to the space of convex Lipschitz functions under certain conditions. Using this, we obtain some dimension results for fractal functions. We also give some bounds on the fractal dimension of fractal functions with the help of oscillation spaces.
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页码：470 / 480
页数：11
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