In [15] M. Schellekens introduced the complexity (quasi-metric) space as a part of the research in Theoretical Computer Science and Topology, with applications to the complexity analysis of algorithms. Later on, S. Romaguera and M. Schellekens ([13]) introduced the so-called dual complexity (quasi-metric) space and established several quasi-metric properties of the complexity space via the anal...

By means of (1.2) and (1.3) each matrix S ∈ SL(2,C) is associated with some matrix S ∈ SO(1, 3,R) so that we can write S = φ(S), see [1], [2], and [3] for detailed description of this construction. Let M be a space-time manifold, i. e. a four-dimensional orientable manifold equipped with a pseudo-Euclidean Minkowski-type metric g and carrying a special smooth geometric structure which is called...

In this paper we consider the so called a cone metric type space, which is a generalization of a cone metric space. We prove some common fixed point theorems for four mappings in those spaces. Obtained results extend and generalize well-known comparable results in the literature. All results are proved in the settings of a solid cone, without the assumption of continuity of mappings.

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...

Abstract In this article, without requiring solidness of the underlying cone, a kind new convergence for sequences in cone b b -metric spaces over Banach algebras and completeness such spaces, namely, wrtn-completeness, are introduced. Under condition that wrtn-complete cones normal, we establish common fixed point the...

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.