Two open problems in the fixed point theory of contractive type mappings on first-countable quasimetric spaces

Abstract

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.