A Study on Fractal Operator Corresponding to Non-stationary Fractal Interpolation Functions

Abstract

This chapter aims to establish the notion of non-stationary-fractal operator and establish some approximations and convergence properties. More specifically, the approximations properties of the non-stationary -fractal polynomials towards a continuous function is discussed. Here a sequence of maps for the non-stationary iterated function systems is used. Further, this chapter shows that the proposed method generalizes the existing stationary interpolant in the sense of iterated function systems. The basic properties of this new notion of interpolant are explored, and its box and Hausdorff dimensions are obtained by comparing it to other well-known results. Additionally, using the method of fractal perturbation of a given function, the associated non-stationary fractal operator is constructed and few of its approximation properties are investigated.