Partial answers of the Asadi et al.’s open question onM-metric spaces with numerical results

FORMAL BALLS IN FUZZY PARTIAL METRIC SPACES

In this paper, the poset $BX$ of formal balls is studied in fuzzy partial metric space $(X,p,*)$. We introduce the notion of layered complete fuzzy partial metric space and get that the poset $BX$ of formal balls is a dcpo if and only if $(X,p,*)$ is layered complete fuzzy partial metric space.

Partial Metric Spaces

As with many mathematical concepts these axioms are chosen to ensure that two things are equal if and only if some property expressible in terms of the concept holds. For a metric space, x = y if and only if d(x, y) = 0. Thus as there is the equality relation x = y in a metric space, so there is what we call an indistancy relation d(x, y) = 0. Axioms M1 and M2 work together to identify equality...

Approximation of Metric Spaces by Partial Metric Spaces

Partial metrics are generalised metrics with non-zero self-distances. We slightly generalise Matthews' original definition of partial metrics, yielding a notion of weak partial metric. After considering weak partial metric spaces in general, we introduce a weak partial metric on the poset of formal balls of a metric space. This weak partial metric can be used to construct the completion of clas...

Coupled Fixed Point Results in Complete Partial Metric Spaces

Some Coupled Fixed Point Results on Partial Metric Spaces