Abstract.

We present a survey of fixed point results in generalized metric spaces (g.m.s.) in the sense of Branciari [Branciari, A., (2000), A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57, 31,37]. Since it may happen that the topology of such space is not Hausdorff, several authors added Hausdorfness (or some other condition) as an additional assumption in order to obtain their results. We show here that such assumptions are usually super°uous. Finally, we state some open questions on the topic.

Keywords:

generalized metric space; quadrilateral inequality; fixed point; Hausdorff space.