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Normed Ordered and ð ¸ -Metric Spaces

Author

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  • Ahmed Al-Rawashdeh
  • Wasfi Shatanawi
  • Muna Khandaqji

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.

Suggested Citation

  • Ahmed Al-Rawashdeh & Wasfi Shatanawi & Muna Khandaqji, 2012. "Normed Ordered and ð ¸ -Metric Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-11, May.
    • Handle: RePEc:hin:jijmms:272137
    DOI: 10.1155/2012/272137
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    References listed on IDEAS

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    1. Dušan Ðukić & Zoran Kadelburg & Stojan Radenović, 2011. "Fixed Points of Geraghty-Type Mappings in Various Generalized Metric Spaces," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-13, December.
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    Cited by:

    1. Huaping Huang, 2019. "Topological Properties of E -Metric Spaces with Applications to Fixed Point Theory," Mathematics, MDPI, vol. 7(12), pages 1-14, December.

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