The family $$\mathcal {N}$$ of n-variate normal distributions is parameterized by the cone positive definite symmetric $$n\times n$$ -matrices and n-dimensional real vector space. Equipped with Fisher information metric, becomes a Riemannian manifold. As such, it diffeomorphic, but not isometric, to space $$\mathrm {Pos}_1(n+1,\mathbb {R})$$ unimodular $$(n+1)\times (n+1)$$ -matrices. computati...

Recently, Azam, Arshad and Beg [4] introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we introduce the notion of c-chainable cone rectangular metric space and we establish a fixed point theorem for uniformly locally contractive mappings in such spaces. An example is given to illustrate...

Let (X,d,K) be a cone b-metric space over a ordered Banach space (E, ) with respect to cone P. In this paper, we study two problems: (1) We introduce a b-metric ρc and we prove that the b-metric space induced by b-metric ρc has the same topological structures with the cone b-metric space. (2) We prove the existence of the coincidence point of two mappings T , f : X → X satisfying a new quasi-co...

For each integer n 2 we construct a compact, geodesic, metric space X which has topological dimension n, is Ahlfors n-regular, satis es the Poincar e inequality, possesses IR as a unique tangent cone at Hn almost every point, but has no manifold points.

The aim of this paper is to obtain extended variants of some common fixed point results in cone metric spaces in the case that the underlying cone is not normal. The first result concerns g-quasicontractions of D. Ilić and V. Rakočević [Common fixed points for maps on cone metric space, J. Math. Anal. Appl. 341 (2008), 876–882], and the second is concerned with HardyRogers-type conditions and e...

Wardowski (2011) in this paper for a normal cone metric space (X, d) and for the family A of subsets of X established a new cone metric H : A × A → E and obtained fixed point of set-valued contraction of Nadler type. Further, it is noticed in the work of Janković et al., 2011 that the fixed-point problem in the setting of cone metric spaces is appropriate only in the case when the underlying co...

There are 339 combinatorial types of generic metrics on six points. They correspond to the 339 regular triangulations of the second hypersimplex ∆(6, 2), which also has 14 non-regular triangulations. 1. The Metric Fan We consider the cone of all metrics on the finite set {1, 2, . . . , n}: Cn = { d ∈ R( n 2 ) : dij ≥ 0 and dij + djk ≥ dik for all 1 ≤ i, j, k ≤ n } . This is a closed convex poin...

Correspondence: [email protected]. edu.tw Department of Applied Mathematics, National Hsinchu University of Education, No. 521 Nanda Rd., Hsinchu City 300, Taiwan Abstract In this article, for a tυs-G-cone metric space (X, G) and for the family A of subsets of X, we introduce a new notion of the tυs H cone metric H with respect to G, and we get a fixed result for the stronger Meir-Keeler-G-cone-t...

In this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in Banach spaces admitting the existence of a lower solution.

Abstract This paper aims to present the concept of multi-valued mappings in fuzzy cone metric spaces and prove some basic lemmas, a Hausdorff metric, fixed point results for set-valued cone-contraction mappings. We theorem rational type cone-contractions spaces. Our extend improve given literature.