  Two open problems in the fixed point theory of quasi metric spaces posed in
[Berinde, V. and Choban, M. M., {\it Generalized distances and their associate
metrics. Impact on fixed point theory}, Creat. Math. Inform. {\bf 22} (2013),
no. 1, 23--32] are considered. We give a complete answer to the first problem,
a partial answer to the second one, and also illustrate the complexity and
relevance of these problems by means of four very interesting and comprehensive
examples.
