In this paper, we introduce new concepts, admissible multivalued hybrid $\mathcal{Z}$-contractions and multivalued hybrid $\mathcal{Z}$-contractions in the framework of $b$-metric spaces and establish sufficient conditions for existence of fixed points for such contractions. A few consequences of our main theorem involving linear and nonlinear contractions are pointed out and discussed by using variants of simulation functions. In the case where our notions are reduced to their single-valued counterparts, the results presented herein complement, unify and generalize a number of significant fixed point theorems due to Branciari, Czerwik, Jachymski, Karapinar and Argawal, Khojasteh, Rhoades, among others. Nontrivial illustrative examples are provided to support the assertions of the obtained results. From application point of view, some fixed point theorems of $b$-metric spaces endowed with partial ordering and graph are deduced and solvability conditions of nonlinear matrix equations are investigated.

中文翻译：

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应用允许的多值混合$ \ mathcal {Z} $收缩

在本文中，我们介绍了新的概念，即在$ b $度量空间框架内的可容许多值混合$ \ mathcal {Z} $压缩和多值混合$ \ mathcal {Z} $压缩，并建立了存在的充分条件这种收缩的固定点。通过使用模拟函数的变体，指出和讨论了我们涉及线性和非线性收缩的主要定理的一些结果。在将我们的概念简化为单值对等的情况下，本文给出的结果补充，统一和归纳了由于Branciari，Czerwik，Jachymski，Karapina和Argawal，Khojasteh，Rhoades等引起的许多重要的不动点定理。提供了非平凡的说明性示例来支持所获得结果的主张。从应用的角度来看，