Abstract The main purpose of this paper is to find some fixed point results with a new approach, particularly in those cases where the existing literature remains silent. More precisely, we introduce partial completeness, f̄-orbitally completeness, a new type of contractions and many other notions. We also ensure the existence of fixed points for non-contraction maps in the class of incomplete partial b-metric spaces. We have reported some examples in support of our results.

中文翻译：

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有序不完全部分b-度量空间背景下的一种新方法

摘要 本文的主要目的是用一种新方法找到一些不动点结果，特别是在现有文献保持沉默的情况下。更准确地说，我们引入了部分完备性、f̄-轨道完备性、一种新型的收缩和许多其他概念。我们还确保在不完整的部分 b 度量空间类中存在非收缩映射的不动点。我们报告了一些例子来支持我们的结果。