Mathematics > Home > Advances in Pure and Applied Mathematics > Issue 2 (May 2021) > Article
N. Vijender
Visvesvaraya of National Institute of Technology Nagpur
India
Published on 26 April 2021 DOI : 10.21494/ISTE.OP.2021.0645
Fractal approximants developed through iterated function systems (IFS) prove more versatile than classical approximants. In this paper, we introduce a new class of fractal approximants using the suitable bounded linear operators defined on the space C(I) of continuous functions and concept of $$$\alpha$$$-fractal functions. The convergence of the proposed fractal approximants towards the original continuous function does not need any condition on the scaling factors. The fractal approximants proposed in this paper possess fractality and convergence simultaneously. Without imposing any condition on the scaling vector, we establish the constrained approximation by the proposed fractal approximants. Existence of Schauder basis of fractal polynomials for the space of continuous functions C(I) is investigated. Using the proposed class of fractal approximants, we develop complex fractal approximants for representation of the square integrable complex-valued functions defined on a real compact interval.
Fractal approximants developed through iterated function systems (IFS) prove more versatile than classical approximants. In this paper, we introduce a new class of fractal approximants using the suitable bounded linear operators defined on the space C(I) of continuous functions and concept of $$$\alpha$$$-fractal functions. The convergence of the proposed fractal approximants towards the original continuous function does not need any condition on the scaling factors. The fractal approximants proposed in this paper possess fractality and convergence simultaneously. Without imposing any condition on the scaling vector, we establish the constrained approximation by the proposed fractal approximants. Existence of Schauder basis of fractal polynomials for the space of continuous functions C(I) is investigated. Using the proposed class of fractal approximants, we develop complex fractal approximants for representation of the square integrable complex-valued functions defined on a real compact interval.
Fractal approximation Complex fractal approximation Fractal dimension Constrained fractal approximation convergence
Fractal approximation Complex fractal approximation Fractal dimension Constrained fractal approximation convergence