The Smoothness of Fractal Interpolation Functions on and on -Series Local Fields

Jing Li and Weiyi Su

Discrete Dynamics in Nature and Society, 2014, vol. 2014, 1-10

Abstract:

A fractal interpolation function on a -series local field is defined, and its -type smoothness is shown by virtue of the equivalent relationship between the Hölder type space and the Lipschitz class Lip . The orders of the -type derivatives and the fractal dimensions of the graphs of Weierstrass type function on local fields are given as an example. The -fractal function on 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 and is given.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:904576

DOI: 10.1155/2014/904576

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