We show that every quasi–norm p on a (real) cancellative cone X induces in a natural way an extended quasi–metric ep on X for which (X, ep) is an extended quasi–metric cone. We prove that the structure of a quasi– normed cone is preserved by bicompletion, under bijective isometries. In fact, we observe that isometries are not necessarily injective in this setting. Some illustrative examples are...

*Correspondence: [email protected] 2School of Mathematics and Computer, Gannan Normal University, Ganzhou, 341000, China Full list of author information is available at the end of the article Abstract In this paper we present some new examples in cone b-metric spaces and prove some fixed point theorems of contractive mappings without the assumption of normality in cone b-metric spaces. The res...

Abstract The space of Euclidean cone metrics on centrically symmetric octahedra with fixed angles ?i < 2 ? , total surface area 1, has a natural hyperbolic metric, and is locally isometric to 3-space. metric completion the ideal tetrahedron whose dihedral are half cone-deficits ? .

* Correspondence: awawdeh@hu. edu.jo Department of Mathematics, Hashemite University, Zarqa 13115, Jordan Abstract In this article, we establish some common fixed and common coincidence point theorems for expansive type mappings in the setting of cone metric spaces. Our results extend some known results in metric spaces to cone metric spaces. Also, we introduce some examples the support the val...

In this paper, we prove that if f is a contractive closed-valued correspondence on a cone metric space (X, d) and there is a contractive orbit {xn} for f at x0 ∈ X such that both {xni} and {xni+1} converge for some subsequence {xni} of {xn}, then f has a fixed point, which generalizes a fixed point theorem for contractive closed-valued correspondences from metric spaces to cone metric spaces.

In this paper, an idea of generalized fuzzy c-distance in fuzzy cone metric space is introduced. A common fixed point theorem is established for a pair of self mappings in fuzzy cone metric spaces by using the concept of generalized fuzzy c-distance. 2010 AMS Classification: : 54A40, 03E72

The notion of triple fixed point was introduced by V.Berinde and M.Borcut [8] and obtained some fixed point theorems in partially ordeded metric spaces. In this paper, we obtain a unique common triple fixed point theorem in partially ordered cone metric spaces in which cone is not necessarilly normal and also mention one supported example.

In this work, we define a weaker Meir–Keeler type function ψ : int P ∪ {0} → int P ∪ {0} in a cone metric space, and under this weaker Meir–Keeler type function, we show the common fixed point theorems of four single-valued functions in cone metric spaces. © 2010 Elsevier Ltd. All rights reserved.

Motivated by recent interest in the spectrum of the Laplacian of incomplete surfaces with isolated conical singularities, we consider more general incomplete m-dimensional manifolds with singularities on sets of codimension at least 2. With certain restrictions on the metric, we establish that the spectrum is discrete and satisfies Weyl’s asymptotic formula. 1. Discreteness of the Spectrum When...

The main contribution in this paper is to introduce an idea of fuzzy cdistance in fuzzy cone metric space. A common fixed point theorem for contraction mapping is established in fuzzy cone metric space by using fuzzy c-distance. Lastly the theorem is justified by a suitable example.