Strong fixed points for Pata-type coupling with application in fractal generation by construction of iterated function systems

Abstract

In this paper, in the first place, a strong coupled fixed point result is established for couplings satisfying Pata-type contractive conditions along with certain corollaries and a supportive illustration. Couplings are combinations of coupled and cyclic maps which have appeared in recent literature and have several applications. The illustrative example shows that the theorem properly extends some of the existing results. In the second part of the paper we construct a special type of iterated function system and, utilizing the coupled fixed point theorem introduced in this work, we show that such systems lead to strong fractal sets. This part of the paper is a part of the Hutchinson–Barnsley theory.