Barnsley-Navascu\'es fractal operators on Banach spaces on the Sierpi\'nski gasket

TL;DR

This paper introduces fractal operators on Banach spaces defined on the Sierpiński gasket, analyzing their properties within operator and approximation theory.

Contribution

It defines new fractal operators inspired by Barnsley and Navascués on various function spaces over the Sierpiński gasket, expanding understanding of their mathematical properties.

Findings

Operators exhibit unique approximation properties.

Analysis reveals operator boundedness and spectral characteristics.

Provides groundwork for future fractal operator applications.

Abstract

In this article, we define fractal operators motivated by the works of Barnsley and Navascu\'es on various function spaces such as energy space, Lebesgue space, and oscillation space on the well-known fractal domain Sierpi\'nski gasket. We further explore the properties of these operators from the perspectives of operator and approximation theory.