In this paper, motivated and inspired by Samet et al., we introduce the notion of generalized weakly contractive mappings in metric spaces and prove the existence and uniqueness of fixed point for such mappings, and we obtain a coupled fixed point theorem in metric spaces. These theorems generalize many previously obtained fixed point results. An example is given to illustrate the main result. Finally, we give applications of our results to fixed point results in partial metric spaces.

中文翻译：

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度量空间中广义弱收缩映射的不动点定理及其应用

在本文中，受Samet等人的启发和启发，我们引入了度量空间中的广义弱压缩映射的概念，并证明了此类映射不动点的存在性和唯一性，并获得了度量空间中的一个耦合不动点定理。这些定理概括了许多先前获得的定点结果。给出一个例子来说明主要结果。最后，我们将结果应用于部分度量空间中的不动点结果。