On the H_ψ-quiver metric and the Banach contraction principle

Resumo

Paper aims to unify in a one-and-only theory several generalizations of the notion of metric as well as its probabilistic versions.
We establish that the following well-known metrics are very special cases namely, Ultrametric, b-Metric, Probabilistic b-Metric,
Branciari Metric, and Probabilistic Generalized Metric. Our approach pushed us to generalize and study
the \textit{Banach contraction principle} in the framework of this unification.