%0 Journal Article
%T Normed Ordered and -Metric Spaces
%A Ahmed Al-Rawashdeh
%A Wasfi Shatanawi
%A Muna Khandaqji
%J International Journal of Mathematics and Mathematical Sciences
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/272137
%X In 2007, Haung and Zhang introduced the notion of cone metric spaces. In this paper, we define an ordered space , and we discuss some properties and examples. Also, normed ordered space is introduced. We recall properties of £¿, and we discuss their extension to . We introduce the notion of -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 -metric spaces. Finally, by extending the notion of a contractive sequence in a real-valued metric space, we show that in -metric spaces, a contractive sequence is Cauchy.
%U http://www.hindawi.com/journals/ijmms/2012/272137/