期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2012
卷号：2012
DOI：10.1155/2012/272137
出版社：Hindawi Publishing Corporation
摘要：In 2007, Haung and Zhang introduced the notion of cone metric spaces. In this paper, we define an ordered space 𝐸, and we discuss some properties and examples. Also, normed ordered space is introduced. We recall properties of ℝ, and we discuss their extension to 𝐸. We introduce the notion of 𝐸-metric spaces and characterize cone metric space. Afterwards, we get generalizations of notions of convergence and Cauchy theory. In particular, we get a fixed point theorem of a contractive mapping in 𝐸-metric spaces. Finally, by extending the notion of a contractive sequence in a real-valued metric space, we show that in 𝐸-metric spaces, a contractive sequence is Cauchy.
