https://doi.org/10.1140/epjs/s11734-023-00866-w
Regular Article
Approximation by the linear fractal interpolation functions with the same fractal dimension
School of Mathematics and Statistics, Nanjing University of Science and Technology, 210094, Nanjing, China
Received:
8
December
2022
Accepted:
3
May
2023
Published online:
1
June
2023
A continuous function defined on a closed interval can be of unbounded variation with certain fractal dimension. Fractal interpolation functions are often used to approximate such functions whose structure seem self affine. In the present paper, a continuous function with non-integer Box dimension has been approximated by certain linear fractal interpolation functions. Both the original function and the linear fractal interpolation functions have the same Box dimension. The interpolation approximation of integer dimensional continuous functions has also been discussed elementary.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
