Fractal dimension of α -fractal function on the Sierpiński Gasket

Abstract

This research article deals with the fractal interpolation function and its box dimension corresponding to a continuous function, defined on the Sierpiński gasket. This research also explores the so-called fractal operator, which is associated with the α-fractal function. Under certain bounds, we shall demonstrate some significant properties of fractal operator such as topological automorphism, fredholm and many others. Among the various applications of fractal operator, the paper also hints at the existence of fractal Schauder basis. © 2021, The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.