Cone Normed Linear Spaces (original) (raw)
Related papers
2016
In this paper, we introduce cone normed linear space, study the cone convergence with respect to cone norm. Finally, we prove the completeness of a finite dimensional cone normed linear space.
Metrizability of Cone Metric Spaces Via Renorming the Banach Spaces
2011
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 valid for cone metric space automatically.
Difference sequence spaces in cone metric space
Proyecciones (Antofagasta), 2014
In this article we introduce the notion of difference bounded, convergent and null sequences in cone metric space. We investigate their different algebraic and topological properties.
A new survey: Cone metric spaces
2018
The purpose of this new survey paper is, among other things, to collect in one place most of the articles on cone (abstract, K-metric) spaces, published after 2007. This list can be useful to young researchers trying to work in this part of functional and nonlinear analysis. On the other hand, the existing review papers on cone metric spaces are updated. The main contribution is the observation that it is usually redundant to treat the case when the underlying cone is solid and non-normal. Namely, using simple properties of cones and Minkowski functionals, it is shown that the problems can be usually reduced to the case when the cone is normal, even with the respective norm being monotone. Thus, we offer a synthesis of the respective fixed point problems arriving at the conclusion that they can be reduced to their standard metric counterparts. However, this does not mean that the whole theory of cone metric spaces is redundant, since some of the problems remain which cannot be treated in this way, which is also shown in the present article.
I - convergence on cone metric spaces
Sarajevo Journal of Mathematics, 2013
The concept of I-convergence is an important generalization of statistical convergence which depends on the notion of an ideal I of subsets of the set N of positive integers. In this paper we introduce the ideas of I-Cauchy and I *-Cauchy sequences in cone metric spaces and study their properties. We also investigate the relation between this new Cauchy type condition and the property of completeness. 2000 Mathematics Subject Classification. 40A05, 40D25. Key words and phrases. Cone metric space, I and I *-convergence, I and I *-Cauchy condition, condition (AP).
Cone normed spaces and weighted means
Mathematical and Computer Modelling, 2010
In this paper, we study the main properties of cone normed spaces, and prove some theorems of weighted means in cone normed spaces.
A unified theory of cone metric spaces
2011
In this paper we develop a unified theory for cone metric spaces over a solid vector space. As an application of the new theory we present full statements of the iterated contraction principle and the Banach contraction principle in cone metric spaces over a solid vector space.