Barnsley-Navascués fractal operators on Banach spaces on the Sierpiński gasket

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