In this paper, we introduce a new concept of fuzzy generalizedcontraction and give a fixed point result for such mappings in the setting of fuzzy M-complete metric spaces. We also give an affirmative partial answer to a question posed by Wardowski [D. Wardowski, Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Set Syst., {bf 222}(2013), 108-114].Some examples are also g...

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...

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...

The purpose of this paper is to introduce the concept of partial rectangular metric spaces as a generalization of rectangular metric and partial metric spaces. Some properties of partial rectangular metric spaces and some fixed point results for quasitype contraction in partial rectangular metric spaces are proved. Some examples are given to illustrate the observed results.