Lp -Approximation Using Fractal Functions on the Sierpiński Gasket

Abstract

We are concerned with the approximation of functions by fractal functions with respect to Lp-norm on the Sierpiński gasket. We define the α-fractal function in Lp space. The properties such as topological isomorphism and many others, which are closely associated with the fractal operator will be discussed in more detail. We also prove the existence of a non-trivial closed invariant subspace for the fractal operator. Additionally, we define set-valued mapping and discuss some useful properties. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.