We introduce a model of the set of all Polish (=separable complete metric) spaces: the cone R of distance matrices, and consider geometric and probabilistic problems connected with this object. The notion of the universal distance matrix is defined and we proved that the set of such matrices is everywhere dense Gδ set in weak topology in the cone R. Universality of distance matrix is the necess...

We introduce the notions of the asymptotic SMK-sequence with respect to the stronger MeirKeeler cone-type mapping ξ : int P ∪ {θ} → 0, 1 and the asymptotic WMK-sequence with respect to the weaker Meir-Keeler cone-type mapping φ : int P ∪ {θ} → int P ∪ {θ} and prove some common fixed point theorems for these two asymptotic sequences in cone metric spaces with regular cone P . Our results general...

Huang and Zhang cite{Huang} have introduced the concept of cone metric space where the set of real numbers is replaced by an ordered Banach space. Shojaei cite{shojaei} has obtained points of coincidence and common fixed points for s-Contraction mappings which satisfy generalized contractive type conditions in a complete cone metric space.In this paper, the notion of complete cone metric ...

In this paper we show that by renorming an ordered Banach space, every cone P can be converted to a normal cone with constant K = 1 and consequently due to this approach every cone metric space is really a metric one and every theorem in metric space is valid for cone metric space automatically.

Recently, Huang and Zhang 1 generalized the concept of a metric space, replacing the set of real numbers by ordered Banach space and obtained some fixed point theorems for mappings satisfying different contractive conditions. Subsequently, the study of fixed point theorems in such spaces is followed by some other mathematicians; see 2–8 . The aim of this paper is to prove a common fixed point t...

*Correspondence: [email protected] 1School of Statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, China 2Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, China Full list of author information is available at the end of the article Abstract In this paper, we introduce the notion of a quasi-contraction restricted with a ...

In this paper, we establish some new coupled fixed point theorems in complete metric spaces, using a new concept of F -invariant set. We introduce the notion of fixed point of N -order as natural extension of that of coupled fixed point. As applications, we discuss and adapt the presented results to the setting of partially ordered cone metric spaces. The presented results extend and complement...

We first establish some existence results concerning approximate coincidence point properties and approximate fixed point properties for various types of nonlinear contractive maps in the setting of cone metric spaces and general metric spaces. From these results, we present some new coincidence point and fixed point theorems which generalize Berinde-Berinde’s fixed point theorem, Mizoguchi-Tak...