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.

在本文中，我们为度量空间的两个子集之间的广义耦合建立了一个强耦合不动点定理。这些是耦合映射的循环推广。从定义耦合的两个子集中收集的两个任意点开始，我们构造两个迭代，每个迭代都收敛到耦合的固定点。进一步表明，这一点是独一无二的。主要结果得到了一个示例的支持，该示例表明我们的结果是现有结果的实际概括。我们还讨论了一个应用程序，在该应用程序中，我们构建了一个迭代函数系统，从而生成了我们在此处定义的强耦合分形。进一步我们通过一个例子来说明这样一个分形集的生成。