The Smoothness of Fractal Interpolation Functions on ℝ and on p-Series Local Fields
A fractal interpolation function on a p-series local field Kp is defined, and its p-type smoothness is shown by virtue of the equivalent relationship between the Hölder type space CσKp and the Lipschitz class Lipσ,Kp. The orders of the p-type derivatives and the fractal dimensions of the graphs of W...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/904576 |
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| author | Jing Li Weiyi Su |
| author_facet | Jing Li Weiyi Su |
| author_sort | Jing Li |
| collection | DOAJ |
| description | A fractal interpolation function on a p-series local field Kp is defined, and its p-type smoothness is shown by virtue of the equivalent relationship between the Hölder type space CσKp and the Lipschitz class Lipσ,Kp. The orders of the p-type derivatives and the fractal dimensions of the graphs of Weierstrass type function on local fields are given as an example. The α-fractal function on ℝ is introduced and the conclusion of its smoothness is improved in a more general case; some examples are shown to support the conclusion. Finally, a comparison between the fractal interpolation functions defined on ℝ and Kp is given. |
| format | Article |
| id | doaj-art-528165da20cd4bac84ec82b5763735b6 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-528165da20cd4bac84ec82b5763735b62025-02-03T06:13:54ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/904576904576The Smoothness of Fractal Interpolation Functions on ℝ and on p-Series Local FieldsJing Li0Weiyi Su1Department of Mathematics, Nanjing University, Nanjing 210093, ChinaDepartment of Mathematics, Nanjing University, Nanjing 210093, ChinaA fractal interpolation function on a p-series local field Kp is defined, and its p-type smoothness is shown by virtue of the equivalent relationship between the Hölder type space CσKp and the Lipschitz class Lipσ,Kp. The orders of the p-type derivatives and the fractal dimensions of the graphs of Weierstrass type function on local fields are given as an example. The α-fractal function on ℝ is introduced and the conclusion of its smoothness is improved in a more general case; some examples are shown to support the conclusion. Finally, a comparison between the fractal interpolation functions defined on ℝ and Kp is given.http://dx.doi.org/10.1155/2014/904576 |
| spellingShingle | Jing Li Weiyi Su The Smoothness of Fractal Interpolation Functions on ℝ and on p-Series Local Fields Discrete Dynamics in Nature and Society |
| title | The Smoothness of Fractal Interpolation Functions on ℝ and on p-Series Local Fields |
| title_full | The Smoothness of Fractal Interpolation Functions on ℝ and on p-Series Local Fields |
| title_fullStr | The Smoothness of Fractal Interpolation Functions on ℝ and on p-Series Local Fields |
| title_full_unstemmed | The Smoothness of Fractal Interpolation Functions on ℝ and on p-Series Local Fields |
| title_short | The Smoothness of Fractal Interpolation Functions on ℝ and on p-Series Local Fields |
| title_sort | smoothness of fractal interpolation functions on r and on p series local fields |
| url | http://dx.doi.org/10.1155/2014/904576 |
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