The paper aims at initiating and exploring the concept of extended metric known as Strong Altering JS-metric, a stronger version JS-metric. interrelation JS-metric with b-metric dislocated has been analyzed some examples have provided. Certain theorems on fixed points for expansive self-mappings in setting complete space also discussed.

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 the study of fixed points of an operator it is useful to consider a more general concept, namely coupled fixed point. Edit In this paper, by using notion partial metric, we introduce a metric space $S$-Hausdorff on the set of all close and bounded subset of $X$. Then the fixed point results of multivalued continuous and surjective mappings are presented. Furthermore, we give a positive resul...

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].

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...

In this paper, we give some results on the common fixed point of self-mappings defined on complete $b$-metric spaces. Our results generalize Kannan and Chatterjea fixed point theorems on complete $b$-metric spaces. In particular, we show that two self-mappings satisfying a contraction type inequality have a unique common fixed point. We also give some examples to illustrate the given results.