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In this paper, we introduce the new concepts of multidimensional Menger probabilistic metric spaces and related fixed point for a pair of mappings T: $\underbrace{X\times X\times\cdots\times X}_{n}\rightarrow X $ and A: $X\rightarrow X$ . Utilizing the properties of the related triangular norm and the compatibility of A with T, some multidimensional common fixed point problems of hybrid probabilistic contractions with a gauge function φ are studied. The obtained results generalize some coupled and triple common fixed point theorems in the corresponding literature. Finally, an example is given to illustrate our main results.

In this paper, we introduce the concepts of generalized probabilistically bounded set $\Omega^{*}$ and Menger-Hausdorff metric $\widetilde{G}^{*}$ in Menger probabilistic G-metric spaces, and prove that $(\Omega^{*},\widetilde{G}^{*},\Delta)$ is also a Menger probabilistic G-metric space. Utilizing these concepts, we establish some common fixed point theorems for three hybrid pairs of mappings satisfying the common property $(E.A)$ in Menger probabilistic G-metric spaces. Finally, an example is given to exemplify the theorems.

In this paper, a new concept of the common property (E.A) for two hybrid pairs of mappings is introduced in Menger PM-spaces. Utilizing this concept, some common fixed point theorems, which shed some new light on the study of fixed point results for hybrid pairs in Menger PM-spaces, are obtained under strict contractive conditions. The corresponding results in metric spaces which generalize many known results are also obtained. Finally, an example is also given to exemplify our main results.