Order-unit-metric spaces

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• 作者：Mert ?a?lar (1)
  Zafer Ercan (2)
  
• 关键词：Cone metric space ; Ordered vector space ; Order unit ; Interior of cone ; Metrizability ; Primary 54E35
• 刊名：Positivity
• 出版年：2014
• 出版时间：September 2014
• 年：2014
• 卷：18
• 期：3
• 页码：557-565
• 全文大小：191 KB
• 参考文献：1. Abbas, M., Jungck, G.: Common fixed point results for noncommuting mappings without continuity in cone metric spaces. J. Math. Anal. Appl. 341(1), 416-20 (2008) CrossRef
  2. Aliprantis, C.D., Tourky, R.: Cones and duality. In: Graduate Studies in Mathematics, vol. 84. American Mathematical Society, Providence (2007)
  3. Bonsall, F.F.: Sublinear functionals and ideals in partially ordered vector spaces. Proc. Lond. Math. Soc. 4(3), 402-18 (1954)
  4. Huang, L.-G., Zhang, X.: Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332(2), 1468-476 (2007) CrossRef
  5. Ili?, D., Rako?evi?, V.: Common fixed points for maps on cone metric space. J. Math. Anal. Appl. 341(2), 876-82 (2008) CrossRef
  6. Jameson, G.: Ordered linear spaces. In: Lecture Notes in Mathematics, vol. 141. Springer, Berlin (1970)
  7. Kadison, R.V.: A representation theory for commutative topological algebra. Mem. Am. Math. Soc. (7), 1-9 (1951)
  8. Khani, M., Pourmadhian, M.: On the metrizability of cone metric spaces. Topol. Appl. 158(2), 190-93 (2011) CrossRef
  9. Anthony, L.: Peressini, Ordered Topological Vector Spaces. Harper & Row, Publishers, New York (1967)
  10. Rezapour, Sh., Hamlbarani, R.: Some notes on the paper: ‘Cone metric spaces and fixed point theorems of contractive mappings- by L.-G. Huang and X. Zhang. J. Math. Anal. Appl. 345(2), 719-24 (2008)
  11. S?nmez, A.: On paracompactness in cone metric spaces. Appl. Math. Lett. 23(4), 494-97 (2010) CrossRef
  12. Willard, S.: General Topology. Addison-Wesley Publishing Co., Reading (1970)
  
• 作者单位：Mert ?a?lar (1)
  Zafer Ercan (2)
  
  1. Department of Mathematics and Computer Science, ?stanbul Kültür University, Bak?rk?y, 34156?, Istanbul, Turkey
  2. Department of Mathematics, Abant ?zzet Baysal University, G?lk?y Kampüsü, 14280?, Bolu, Turkey
  
• ISSN：1572-9281

文摘

We study the concept of cone metric space in the context of ordered vector spaces by setting up a general and natural framework for it.