Fractals in extended b-metric space.

Abstract

Iterated function systems are method of constructing fractals, which are based on the mathematical foundations laid by Hutchinson[1] and  Barnsley[2]. Formally an Iterated function systems is a finite set of ‘contraction mappings’, on a complete metric space X. In this paper we construct a fractal set of Iterated function systems, which in our case are a collection of mappings defined in an extended b-metric space, of compact subsets of the space. We will prove that the Hutchinson operator defined with the help of a finite family of ‘generalized F-contraction mappings’ on a complete extended b- metric space is itself a generalized F- contraction mapping on a family of compact subsets of X. Then by successive application of a generalized F-Hutchinson operator we obtain a final fractal in an extended b- metric space