Smoothness analysis and approximation aspects of non-stationary bivariate fractal functions

The present note aims to establish the notion of non-stationary bivariate alpha-fractal functions and discusses some of their approximation properties. We see that using a sequence of iterated function systems generalizes the existing stationary fractal interpolation function (FIF). Also, we show the existence of Borel probability fractal measures supported on the graph of the non-stationary fractal function. Further, we define a fractal operator associated with the constructed non-stationary FIFs, and many applications of this operator such as fractal approximation and the existence of fractal Schauder bases are observed. In the end, we study the constrained approximation with the proposed interpolant.