Zipper Fractal Functions with Variable Scalings

Authors : VİJAY, A K B CHAND

Pages : 481-501

Doi:10.31197/atnaa.1149689

View : 16 | Download : 4

Publication Date : 2022-12-30

Article Type : Research Paper

Abstract :Zipper fractal interpolation function insert ignore into journalissuearticles values(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,∞);.
Keywords : Fractals, zipper smooth fractal function, topological isomorphism, Schauder basis, linear operator