A quasimetric on a quasimetric space can be referred to as a distance function in the same way as a metric on a metric space.
Related Journals of Fuzzy Quasi-Metric Space
Computational Materials Science, Journal of Physical Mathematics, Research & Reviews: Journal of Statistics and Mathematical Sciences, Biometrics & Biostatistics Journal, Journal of Computational and Applied Mathematics, Engineering Analysis with Boundary Elements, Numerical Methods for Partial Differential Equations and BIT Numerical Mathematics.
Journal of Applied & Computational Mathematics received 1282 citations as per Google Scholar report