An alternative characterization of probabilistic Menger spaces with H-type triangular norms

The class of H-type triangular norms was introduced for the first time by Hadžić in 1978. In this paper a new characteristic property of the H-type triangular norm is presented. By virtue of this alternative characterization, the continuity of quasi-metrics and quasi-norms is studied and some properties of the probabilistic Menger spaces with this triangular norm are considered. As applications new fixed point and fixed degree theorems for probabilistic nonlinear contractions and fuzzy mappings are given.