Lp-Approximation Using Fractal Functions on the Sierpiriski Gasket

We are concerned with the approximation of functions by fractal functions with respect to L-p-norm on the Sierphiski gasket. We define the alpha-fractal function in L-p 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.