Zipper Fractal Functions with Variable Scalings
Zipper fractal interpolation function (ZFIF) is a generalization of fractal interpolation function through an improved version of iterated function system by using a binary parameter called a signature. The signature allows the horizontal scalings to be negative. ZFIFs have a complex geometric str...
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| Format: | Article |
| Language: | English |
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ATNAA
2022-07-01
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| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/2560914 |
| _version_ | 1797917010591481856 |
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| author | Vijay A.K.B. Chand |
| author_facet | Vijay A.K.B. Chand |
| author_sort | Vijay |
| collection | DOAJ |
| description | Zipper fractal interpolation function (ZFIF) is a generalization of fractal interpolation function through an
improved version of iterated function system by using a binary parameter called a signature. The signature
allows the horizontal scalings to be negative. ZFIFs have a complex geometric structure, and they can
be non-differentiable on a dense subset of an interval I. In this paper, we construct k-times continuously
differentiable ZFIFs with variable scaling functions on I. Some properties like the positivity, monotonicity,
and convexity of a zipper fractal function and the one-sided approximation for a continuous function by a
zipper fractal function are studied. The existence of Schauder basis of zipper fractal functions for the space
of k-times continuously differentiable functions and the space of p-integrable functions for p ∈ [1, ∞) are
studied. We introduce the zipper versions of full Müntz theorem for continuous function and p-integrable
functions on I for p ∈ [1, ∞).
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| first_indexed | 2024-04-10T13:07:36Z |
| format | Article |
| id | doaj.art-d85d80279f1547c7ab665378390e08e0 |
| institution | Directory Open Access Journal |
| issn | 2587-2648 |
| language | English |
| last_indexed | 2024-04-10T13:07:36Z |
| publishDate | 2022-07-01 |
| publisher | ATNAA |
| record_format | Article |
| series | Advances in the Theory of Nonlinear Analysis and its Applications |
| spelling | doaj.art-d85d80279f1547c7ab665378390e08e02023-02-15T16:12:56ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482022-07-016448150110.31197/atnaa.1149689Zipper Fractal Functions with Variable ScalingsVijayA.K.B. ChandZipper fractal interpolation function (ZFIF) is a generalization of fractal interpolation function through an improved version of iterated function system by using a binary parameter called a signature. The signature allows the horizontal scalings to be negative. ZFIFs have a complex geometric structure, and they can be non-differentiable on a dense subset of an interval I. In this paper, we construct k-times continuously differentiable ZFIFs with variable scaling functions on I. Some properties like the positivity, monotonicity, and convexity of a zipper fractal function and the one-sided approximation for a continuous function by a zipper fractal function are studied. The existence of Schauder basis of zipper fractal functions for the space of k-times continuously differentiable functions and the space of p-integrable functions for p ∈ [1, ∞) are studied. We introduce the zipper versions of full Müntz theorem for continuous function and p-integrable functions on I for p ∈ [1, ∞). https://dergipark.org.tr/tr/download/article-file/2560914fractalszipper smooth fractal functiontopological isomorphismschauder basis linear operator |
| spellingShingle | Vijay A.K.B. Chand Zipper Fractal Functions with Variable Scalings Advances in the Theory of Nonlinear Analysis and its Applications fractals zipper smooth fractal function topological isomorphism schauder basis linear operator |
| title | Zipper Fractal Functions with Variable Scalings |
| title_full | Zipper Fractal Functions with Variable Scalings |
| title_fullStr | Zipper Fractal Functions with Variable Scalings |
| title_full_unstemmed | Zipper Fractal Functions with Variable Scalings |
| title_short | Zipper Fractal Functions with Variable Scalings |
| title_sort | zipper fractal functions with variable scalings |
| topic | fractals zipper smooth fractal function topological isomorphism schauder basis linear operator |
| url | https://dergipark.org.tr/tr/download/article-file/2560914 |
| work_keys_str_mv | AT vijay zipperfractalfunctionswithvariablescalings AT akbchand zipperfractalfunctionswithvariablescalings |