The purpose of this paper is to define a rational orbitally ()-contraction and prove some new results in the context of -metric spaces. Our results extend, generalize, and unify some known results in the literature. As application of our main result, we investigate the solution of Fredholm integral inclusion. We also provide an example to substantiate the advantage and usefulness of obtained results.

中文翻译：

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Rational Orbitally ()-收缩与应用程序的不动点结果

本文的目的是定义一个有理轨道（)-收缩并证明了-度量空间上下文中的一些新结果。我们的结果扩展、概括和统一了文献中的一些已知结果。作为我们主要结果的应用，我们研究了 Fredholm 积分包含的解。我们还提供了一个例子来证实所获得结果的优势和有用性。