In this manuscript, using the concept of a couple $\left[fh\right]$ called generalized upper-class of type-III and $({\alpha }_{\ast },{\eta }_{\ast }{)}_{\text{β}}$-contraction, multi-valued fixed-point results are established in metric spaces. Our results generalized many results in the current literature. Further our methods can be applicable to the study of consensus problems. For the authenticity of the presented work, example and existence theorem for Fredholm-type integral inclusion are also discussed.

中文翻译：

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集值定点结果及其在Fredholm型积分包含中的应用

在本手稿中，使用了一对夫妇的概念 $\left[FH\right]$ 称为III型广义上层 $（{\alpha }_{\ast }，{\eta }_{\ast }{）}_{\text{β}}$-收缩，在度量空间中建立多值定点结果。我们的结果概括了当前文献中的许多结果。此外，我们的方法可以适用于共识问题的研究。为了保证本文工作的真实性，还讨论了Fredholm型积分包含的实例和存在性定理。