Certain Results Concerning the Iterative Function System

Invention of wavelets and fractals have revolutionized several areas of emerging technologies, especially image processing and scientific computing. The iterated function system [2-4,13,17,18,20,25,26,29], inverse problem of images [5,14-16] and wavelet-based numerical methods [6,7,10,19,22,23] are basic in-gredients of these exciting developments. The iterated function system and the collage theorem are among the basic mathematical tools which are consequences of the Banach contraction fixed point theorem. In one of the sections of this paper we have generalized these two theorems applying a generalization of the Banach contraction fixed point theorem due to Edelstein [11]. In the other section we have studied the inverse problem of images by the iterative function system with grey-level in the context of Besov space, extending a result of Forte and Vrscay [16].