Within this manuscript we generalize the two recently obtained results of O. Popescu and G. Stan, regarding F-contractions in complete, ordinary metric space to 0-complete partial metric-like space. As Stan use less conditions than D. Wardovski did his paper from 2012, introduce, with help one our lemmas, a new method proving fixed point theory. Requiring that function F only be strictly increa...

In this paper, we introduce the notions of ordered F -(F, h)-contraction and subcontraction in the setting of partial metric spaces. Some fixed point theorems for ordered F -(F, h)-contraction and subcontraction in 0-f -orbitally complete partial metric spaces are proved. Our results generalize some recent results of metric and partial metric spaces into the 0-f -orbitally complete partial metr...

Using the notion of formal ball, we present a few new results in the theory of quasi-metric spaces. With no specific order: every continuous Yoneda-complete quasi-metric space is sober and convergence Choquet-complete hence Baire in its d-Scott topology; for standard quasi-metric spaces, algebraicity is equivalent to having enough center points; on a standard quasi-metric space, every lower sem...