A probabilistic semi-metric space (S, F ) is said to be of class H ([5]) if there exists a metric d on S such that, for t > 0, d(p, q) < t ⇔ Fpq(t) > 1− t. We will prove that (S, F ) is of class H iff the mapping K, defined on S × S by K (p, q) = sup{t ≥ 0 | t ≤ 1− Fpq(t)} is a metric on S. Two fixed point theorems for multivalued contractions in probabilistic metric spaces are also proved. Inc...

In this paper, we introduce a new concept in set-valued mappings which we have called condition $(UHS)$. Then, adding this condition to a new type of contractive set-valued mappings, recently has been introduced by Amini-Harandi [Fixed and coupled fixed points of a new type contractive set-valued mapping in complete metric spaces, Fixed point theory and applications, 215 (2012)], we prove that ...

Recall that a metric space M is said to be complete if every Cauchy sequence in M converges to a limit in M . Not all metric spaces are complete, but it is a fact that all metric spaces can be “completed”, in a way that preserves the essential structure of the metric space. If the space in question is a normed linear space this process completes the space to a Banach space, and an inner product...

the sequential $p$-convergence in a fuzzy metric space, in the sense of george and veeramani, was introduced by d. mihet as a weaker concept than convergence. here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. in such a case $m$ is called an $s$-fuzzy metric. if $(n_m,ast)$ is a fuzzy metri...

Sherwood [Z] showed that every Menger space with continuous t-norm has a completion which is unique up to isometry. Since fuzzy metric spaces resemble in some respects probabilistic metric spaces it is to be expected that at least some fuzzy metric spaces have a completion. The purpose of this paper is to prove that. We need the following definitions. For the definition and properties of a fuzz...

Network Coordination Systems (NCS) are powerful mechanisms to efficiently predict the network latency of pairwise hosts in Internet without directly network measurement between them. Each host is embedded into a distance space where the latency between nodes is calculated according to the distant function defined by the space with assigned coordination of hosts. In terms of the properties of di...

The main bottleneck of the research in metric space searching is the so-called curse of dimensionality, which makes the task of searching some metric spaces intrinsically difficult, whatever algorithm is used. A recent trend to break this bottleneck resorts to probabilistic algorithms, where it has been shown that one can find 99% of the elements at a fraction of the cost of the exact algorithm...

We construct a complete metric space M of cardinality continuum such that every non-singleton closed separable subset fails to be Lipschitz retract M. This provides analogue the various classical and recent examples Banach spaces failing have linearly complemented subspaces prescribed smaller density character.