Let S be the unit sphere in the Euclidean space R, and let e be the standard metric on S induced from R. Suppose that (u, ρ) are the spherical coordinates in R, where u ∈ S, ρ ∈ [0,∞). By choosing the smooth function φ(ρ) := sinh ρ on [0,∞) we can define a Riemannian metric h on the set {(u, ρ) : u ∈ S, 0 ≤ ρ < ∞} as follows h = dρ + φ(ρ)e. This gives the space form R(−1) which is the hyperboli...

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].

In this note, we announce some results showing unexpected similarities between the moduli spaces of constant curvature metrics on 2-manifolds (the Riemann moduli space) and moduli spaces of Einstein metrics on 4manifolds. Let J? denote the moduli space of Einstein metrics of volume 1 on a compact, orientable 4-manifold M. If J£\ denotes the space of smooth Riemannian metrics of volume 1 on M, e...

For a given metric space (S, d), let us use the term “standard σ-field” to denote the σ-field S of subsets of S generated by the open balls (in the metric d). A function f : S×S×S× . . .→ S is “measurable” (with respect to S) if for every set A ∈ S one has that f−1(A) is a member of S×S×S×. . . , the product σ-field on S × S × S × . . . . Suppose B is a separable real Banach space. Suppose (Ω,F...

In this paper, the notion of $psi -$weak contraction cite{Rhoades} isextended to fuzzy metric spaces. The existence of common fixed points fortwo mappings is established where one mapping is $psi -$weak contractionwith respect to another mapping on a fuzzy metric space. Our resultgeneralizes a result of Gregori and Sapena cite{Gregori}.

The purpose of this short note is to consider much shorter and nicer proofs about fixed point results on b-metric spaces via b-simulation function introduced very recently by Demma et al. [M. Demma, R. Saadati, P. Vetro, emph{Fixed point results on b-metric space via Picard sequences and b-simulation functions}, Iranian J. Math. Sci. Infor. 11 (1) (2016) 123--136].

In this paper is introduced a new type of generalization of metric spaces called $S_b$ metric space. For this new kind of spaces it has been proved a common fixed point theorem for four mappings which satisfy generalized contractive condition. We also present example to confirm our theorem.

We present the ‘Basic S*’ algorithm for computing shortest path through a metric simplicial complex. In particular, given a metric graph, G, which is constructed as a discrete representation of an underlying configuration space (a larger “continuous” space/manifold typically of dimension greater than one), we consider the Rips complex, R(G), associated with it. Such a complex, and hence shortes...

Let $(X,d)$ be an infinite compact metric space, let $(B,parallel . parallel)$ be a unital Banach space, and take $alpha in (0,1).$ In this work, at first we define the big and little $alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $alpha$-lipschitz $B$-valued operator algebra, $lip_{alpha}(X,B)$. Then we characterize its second dual space.

and Applied Analysis 3 effectively larger than that of the ordinary conemetric spaces. That is, every cone metric space is a cone b-metric space, but the converse need not be true. The following examples show the above remarks. Example 7. Let X = {−1, 0, 1}, E = R, andP = {(x, y) : x ≥ 0, y ≥ 0}. Define d : X × X → P by d(x, y) = d(y, x) for all x, y ∈ X, d(x, x) = θ, x ∈ X, and d(−1, 0) = (3, ...