The motivation of the present paper is to introduce and establish some new fixed point results for monotone multivalued functions in partially ordered complete $D^{*}$ -metric spaces, where the partial ordered set $(X,\leq )$ is obtained via a pair of functions $( \Upsilon,\Omega )$ . Moreover, several existence and uniqueness coupled fixed point theorems of mappings satisfying contractive conditions have been investigated and verified in the setting of partially ordered complete $D^{*}$ -metric spaces by using the concept of integral type contractions with respect to partially ordered $D^{*}$ -metric space. Furthermore, we present appropriate examples as an application for our main results. Our results generalize the work of Ghasab, Majani, and Rad on the study of integral type contraction and coupled fixed point theorems in the ordered G-metric spaces.

中文翻译：

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单调多值整型收缩映射定点结果的一些应用

本文的动机是介绍并建立偏序完备 $D^{*}$ 度量空间中单调多值函数的一些新的不动点结果，其中获得偏序集合 $(X,\leq )$通过一对函数 $( \Upsilon,\Omega )$ 。此外，利用偏序积分型收缩的概念，在偏序完备$D^{*}$-度量空间的设置下，研究并验证了满足收缩条件的映射的存在唯一性耦合不动点定理$D^{*}$ - 度量空间。此外，我们还提供了适当的例子作为我们主要结果的应用。我们的结果概括了 Ghasab、Majani 的工作，