Analysis of non-linear fractal functions on PCF self-similar sets
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915288487821312 |
|---|---|
| author | Shah, Aaryan Dharmesh Jha, Sangita Mondal, Anarul Islam |
| author_facet | Shah, Aaryan Dharmesh Jha, Sangita Mondal, Anarul Islam |
| contents | This article deals with (1) the construction of a general non-linear fractal interpolation function on PCF self-similar sets, (2) the energy and normal derivatives of uniform non-linear fractal functions, (3) estimation of the bound of box dimension of the proposed fractal functions on the Sierpinski gasket and the von-Koch curve. Here, we present a more general framework to construct the attractor and the functions on the PCF self-similar sets using the Edelstein contraction, which broadens the class of functions. En route, we calculate the upper and lower box dimensions of the graph of non-linear interpolant. Finally, we provide several graphical and numerical examples for illustration of the construction and estimate the dimensions for different data sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of non-linear fractal functions on PCF self-similar sets Shah, Aaryan Dharmesh Jha, Sangita Mondal, Anarul Islam Dynamical Systems Functional Analysis This article deals with (1) the construction of a general non-linear fractal interpolation function on PCF self-similar sets, (2) the energy and normal derivatives of uniform non-linear fractal functions, (3) estimation of the bound of box dimension of the proposed fractal functions on the Sierpinski gasket and the von-Koch curve. Here, we present a more general framework to construct the attractor and the functions on the PCF self-similar sets using the Edelstein contraction, which broadens the class of functions. En route, we calculate the upper and lower box dimensions of the graph of non-linear interpolant. Finally, we provide several graphical and numerical examples for illustration of the construction and estimate the dimensions for different data sets. |
| title | Analysis of non-linear fractal functions on PCF self-similar sets |
| topic | Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2505.10455 |