A Note on Complex-Valued Fractal Functions on the Sierpiński Gasket

Abstract

Traditional non-recursive approximation methods are less versatile than fractal interpolation and approximation approaches. The concept of fractal interpolation functions (FIFs) have been found to be an effective technique for generating interpolants and approximants which can approximate functions generated by nature that exhibit self-similarity when magnified. Using an iterated function system (IFS), Barnsley discovered the FIFs, which is the most prominent approach for constructing fractals. In this article, we investigate some properties of the real-valued fractal operator and the complex-valued fractal operator defined on the Sierpiński gasket (SG in short). We also calculate the bound for the perturbation error on SG. Furthermore, we prove that the complex-valued fractal operator is bounded. In the last part, we establish the connection between the norm of the real-valued fractal operator and the complex-valued fractal operator. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.