Fixed points of generalized cyclic contractions without continuity and application to fractal generation

Abstract

In this paper, we define a generalized cyclic contraction and prove a unique fixed point theorem for these contractions. An illustrative example is given, which shows that these contraction mappings may admit the discontinuities and also that an existing result in the literature is effectively generalized by the theorem. We apply the fixed point result for generation of fractal sets through construction of an iterated function system and the corresponding Hutchinsion–Barnsley operator. The above construction is illustrated by an example. The study here is in the context of metric spaces.