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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.

Multidimensional common fixed point theorems under probabilistic φ-contractive conditions in multidimensional Menger probabilistic metric spaces