- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 6 Issue: 4
- Zipper Fractal Functions with Variable Scalings
Zipper Fractal Functions with Variable Scalings
Authors : . Vijay, A. K. B. Chand
Pages : 481-501
Doi:10.31197/atnaa.1149689
View : 5 | Download : 3
Publication Date : 2022-12-30
Article Type : Research
Abstract :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,∞).Keywords : Fractals, zipper smooth fractal function, topological isomorphism, Schauder basis, linear operator