Two type quasi-contractions on quasi metric spaces and some fixed point results

In this paper, we introduce new concepts of quasi-contractions of type (A) and of type (B) in a quasi metric space and we present the differences between of them. Then we present some fixed point results. In the light of the theorems it is shown that, although the Hausdorffness condition of quasi metric space is needed for the mapping of quasi contraction of type (A), it is not necessary to guarantee the existence of fixed point for the mapping of quasi contraction of type (B).