On Dimension of Fractal Functions on Product of the Sierpiński Gaskets and Associated Measures

In this article, our aim is to estimate the fractal dimensions of the graphs of fractal interpolation functions (FIFs) on the product of two Sierpiński gaskets. To achieve this, we employ the Hölder function spaces. We also define a fractal operator on Hölder spaces originated from the FIFs and establish some operator-theoretic properties such as bounded below and invariant subspaces of it. Additionally, we provide bounds on the Hausdorff dimensions of the invariant measures that are supported on the graphs of these FIFs.