In this study, we introduce the concept of $\theta$-expansive mapping in ordered metric spaces and prove a fixed point theorem for such mappings. We give some fixed point results for $\theta$-expansive mapping in metric spaces and prove fixed point theorems for such mappings. These results extend the main results of many comparable results from the current literature. We also obtain a common fixed point theorem of two weakly compatible mappings in metric spaces. Finally, the examples are presented to support the new theorems and results proved.

中文翻译：

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度量空间中扩展映射的不动点结果

在这项研究中，我们介绍了 $\theta$-有序度量空间中的-扩展映射，并证明此类映射的不动点定理。我们给出一些定点结果$\theta$度量空间中的可扩展映射，并证明此类映射的不动点定理。这些结果扩展了当前文献中许多可比较结果的主要结果。我们还获得了度量空间中两个弱兼容映射的公共不动点定理。最后，给出了实例以支持新的定理并证明了结果。