A Novel Generalization of Strong Probabilistic $b$-Metric Spaces and Fixed Point Theorems

The controlled strong probabilistic (fuzzy) $b$-metric space is a novel concept we introduce in this study. We also demonstrate some of its fundamental topological properties and provide examples. In this context, a new result of fixed point property was proved for the probabilistic $\omega$-contraction mapping on these kinds of spaces. Many prior findings in the literature are generalized and unified by our findings. Some related results are also offered to illuminate further the fundamental theorem in ordinary controlled strong $b$-metric spaces.