Functional equations related to weightable quasi-metrics

Starting from the definition of a weightable quasi-metric we observe that several functional equations are induced in a natural way. Studying these equations we characterize weightable quasi-metrics and show that they define representable total preorders. We also analyze how to retrieve weightable quasi-metrics from real-valued functions satisfying suitable functional equations. 2000 AMS Classification: 39B52, 54E35, 54F05, 06A06.