In the present paper, we introduce the concept of F-contraction on vector-valued metric space. Then, we achieved a fixed point result that includes the famous Perov fixed point theorem as properly. We provided a nontrivial and illustrative example showing this fact. Finally, we give an existence result for semilinear operator system in a Banach space.

中文翻译：

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Perov F型收缩的不动点结果及其应用

在本文中，我们介绍了向量值度量空间上的F-压缩的概念。然后，我们获得了一个定点结果，其中适当地包含了著名的Perov定点定理。我们提供了一个简单而说明性的示例来说明这一事实。最后，我们给出了Banach空间中半线性算子系统的存在性结果。