Fractal polynomials On the Sierpi\'nski gasket and some dimensional results

TL;DR

This paper investigates fractal polynomials on the Sierpiński gasket, analyzing their approximation properties, fractal dimensions, and related operator characteristics to advance understanding of fractal function spaces.

Contribution

It introduces new properties of fractal operators on the Sierpiński gasket and examines approximation and dimensional aspects of fractal polynomials on this fractal set.

Findings

Established properties of fractal operators on SG

Analyzed best approximation of fractal polynomials on SG

Estimated fractal dimensions of fractal function graphs

Abstract

In this paper, we explore some significant properties associated with a fractal operator on the space of all continuous functions defined on the Sierpi\'nski Gasket (SG). We also provide some results related to constrained approximation with fractal polynomials and study the best approximation properties of fractal polynomials defined on the SG. Further we discuss some remarks on the class of polynomials defined on the SG and try to estimate the fractal dimensions of the graph of $\alpha$- fractal function defined on the SG by using the oscillation of functions.