We first prove one of the most basic inequalities on a b-metric space. And then we prove some fixed point theorems. We also consider two similar conditions; one implies the Cauchyness on sequences but the other does not.

The purpose of this paper is to establish some fixed point results for a class generalized $(\phi, \psi)$-weak contraction mapping in partially ordered $b$-metric space. This necessarily have unique under relation Also, the common and coincidence points self mappings are presented. These generalize extend an existing literature. Some illustrations given at end support results.

The Poisson kernels and relations between them for a massive scalar field in a unit ball B with Hua’s metric and conformal flat metric are obtained by describing the B as a submanifold of an (n+1)-dimensional embedding space. Global geometric properties of the AdS space are discussed. We show that the (n+1)-dimensional AdS space AdSn+1 is isomorphic to RP 1 ×Bn and boundary of the AdS is isomor...

A space X is cometrizable if X has a coarser metric topology such that each point of X has a neighborhood base of metric closed sets. Most examples in the literature of spaces obtained by modifying the topology of the plane or some other metric space are cometrizable. Assuming the Proper Forcing Axiom (PFA) we show that the following statements are equivalent for a cometrizable space X : (a) X ...

We introduce the concept of $b$-$\theta$-metric space as a generalization $\theta$-metric and investigate some its properties. Then, we establish fixed point theorem in spaces via $b$-simulation functions. Thus, deduce Banach type such spaces. Also, discuss results relation to existing ones.

In this paper, we firstly introduce the definition of fuzzy metric sets, and discuss properties induced by Hausdorff metric. Then prove limit theorems for set-valued random variables in space; convergence is about The work an extension from classical results to space.

Sometimes there might be another metric space (N, ρ(u, v)) in play, and we may introduce a subscript as in BN(w, s) to indicate in which metric space the ball is defined. Let us say that a metric space (M, d(x, y)) is a happy fractal if the following three conditions are satisfied. First, M is complete as a metric space. Second, there is a constant C1 > 0 so that for each pair of points x, y in...

We prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of Aliouche, et al. [2], Rao et al. [14] and [15].