Normed Ordered and ð ¸ -Metric Spaces

Ahmed Al-Rawashdeh, Wasfi Shatanawi and Muna Khandaqji

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-11

Abstract:

In 2007, Haung and Zhang introduced the notion of cone metric spaces. In this paper, we define an ordered space ð ¸ , and we discuss some properties and examples. Also, normed ordered space is introduced. We recall properties of â„ , and we discuss their extension to ð ¸ . We introduce the notion of ð ¸ -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 ð ¸ -metric spaces. Finally, by extending the notion of a contractive sequence in a real-valued metric space, we show that in ð ¸ -metric spaces, a contractive sequence is Cauchy.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:272137

DOI: 10.1155/2012/272137

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