Strong fixed points of [formula omitted]-couplings and generation of fractals

Abstract

In this paper we establish a strong coupled fixed point theorem for a generalized coupling between two subsets of a metric space. These are cyclic generalizations of coupled mappings. Starting from two arbitrary points collected from the two subsets between which the coupling is defined, we construct two iterations each of which converges to the coupled fixed point. Further it is shown that such a point is unique. The main result is supported with an example which shows that our result is an actual generalization of an existing result. We also discuss an application in which we construct an iterated function system leading to the generation of a strong coupled fractal which we define here. Further we illustrate the generation of such a fractal set through an example.