In this paper, we introduce the notion of generalized -contractions which enlarge the class of ℒ-contractions initiated by Cho in 2018. Thereafter, we also, define the notion of -contractions. Utilizing our newly introduced notions, we establish some new fixed-point theorems in the setting of complete Branciari’s metric spaces, without using the Hausdorff assumption. Moreover, some examples and applications to boundary value problems of the fourth-order differential equations are given to exhibit the utility of the obtained results.

中文翻译：

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Branciari度量空间中的新压缩映射及其不动点

在本文中，我们介绍了广义-收缩的概念，该概念扩大了Cho在2018年发起的ℒ-收缩的类别。此后，我们还定义了-收缩的概念。利用我们新引入的概念，我们在不使用Hausdorff假设的情况下，在完整Branciari度量空间的设置中建立了一些新的不动点定理。此外，给出了一些实例和对四阶微分方程的边值问题的应用，以展示所得结果的实用性。