A novel approach to Banach contraction principle in extended quasi-metric spaces

The purpose of this note is to give a natural approach to the extensions of the Banach contraction principle in metric spaces endowed with a partial order, a directed graph or a binary relation in terms of extended quasimetric. This novel approach is new and may open the door to other new fixed point theorems. The case of multivalued mappings is also discussed and an analogue result to Nadler s fixed point theorem in extended quasi-metric spaces is given.