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ON FRACTAL DIMENSIONS OF FRACTAL FUNCTIONS USING FUNCTION SPACES

Part of: Approximations and expansions Classical measure theory

Published online by Cambridge University Press:  08 August 2022

SUBHASH CHANDRA  and
SYED ABBAS Open the ORCID record for SYED ABBAS [Opens in a new window]
SUBHASH CHANDRA
Affiliation:
School of Basic Sciences, Indian Institute of Technology Mandi, Kamand, Himachal Pradesh 175005, India e-mail: sahusubhash77@gmail.com
SYED ABBAS*
Affiliation:
School of Basic Sciences, Indian Institute of Technology Mandi, Kamand, Himachal Pradesh 175005, India
*
e-mail: sabbas.iitk@gmail.com
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Abstract

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.

Keywords

fractal interpolation functionsconvex-Lipschitz spaceoscillation spaceHausdorff dimensionbox dimension

MSC classification

Primary: 28A80: Fractals
Secondary: 33C47: Other special orthogonal polynomials and functions 41A30: Approximation by other special function classes
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 106 , Issue 3 , December 2022 , pp. 470 - 480
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The first author received financial support from CSIR, India with grant no: 09/1058(0012)/2018-EMR-I.

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