Menger-Hausdorff metric and common fixed point theorems in Menger probabilistic G -metric spaces

摘要

In this paper, we introduce the concepts of generalized probabilistically bounded set Ω ∗ $Omega^{*}$ and Menger-Hausdorff metric G ˜ ∗ $widetilde{G}^{*}$ in Menger probabilistic G-metric spaces, and prove that ( Ω ∗ , G ˜ ∗ , Δ ) $(Omega^{*},widetilde{G}^{*},Delta)$ 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 ) $(E.A)$ in Menger probabilistic G-metric spaces. Finally, an example is given to exemplify the theorems.