Zipper Fractal Functions with Variable Scalings

Yıl 2022, , 481 - 501, 30.12.2022

. Vijay A. K. B. Chand

https://doi.org/10.31197/atnaa.1149689

Cited By: 4

Öz

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,∞).

Anahtar Kelimeler

Fractals, zipper smooth fractal function, topological isomorphism, Schauder basis, linear operator

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