Let (M, ∂M) be a compact 3-manifold with boundary which admits a complete, convex co-compact hyperbolic metric. We are interested in the following question: Question A Let h be a (non-smooth) metric on ∂M , with curvature K > −1. Is there a unique hyperbolic metric g on M , with convex boundary, such that the induced metric on ∂M is h ? There is also a dual statement: Question B Let h be a (non...

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

Objective: The purpose of this paper is to prove some common fixed-point theorems satisfying the rational type contractive condition in frame work complex valued b metric spaces. Methodology: Some well-known result we studied –metric spaces and replaced constant by control function obtain new fixed point also proving uniqueness for a pair mappings. Findings: Results based on are derived context...

Proving  fixed point theorem in a fuzzy metric space is not possible for  Meir-Keeler contractive mapping. For this, we introduce the notion of $c_0$-triangular fuzzy metric space. This new space allows us to prove some fixed point theorems for  Meir-Keeler contractive mapping. As some pattern we introduce the class of $alphaDelta$-Meir-Keeler contractive and we establish some results of fixed ...

in this paper we define weak $f$-contractions on a‎ ‎metric space into itself by extending $f$-contractions‎ ‎introduced by d‎. ‎wardowski (2012) and provide some fixed point‎ ‎results in complete metric spaces and in partially ordered complete ‎generalized metric spaces‎. ‎some relationships between weak‎ ‎$f$-contractions and $fi$-contractions are highlighted‎. ‎we also ‎give some application...

A new method to study the intrinsic color and luminosity of type Ia supernovae (SNe Ia) is presented. A metric space built using principal component analysis (PCA) on spectral series SNe Ia between −12.5 and +17.5 days from B maximum is used as a set of predictors. This metric space is built to be insensitive to reddening. Hence, it does not predict the part of color excess due to dust-extincti...

We introduce a new type of Caristi’s mapping on partial metric spaces and show that a partial metric space is complete if and only if every Caristi mapping has a fixed point. From this result we deduce a characterization of bicomplete weightable quasi-metric spaces. Several illustrative examples are given.