Various generalizations of metric spaces and fixed point theorems
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  • 作者：Tran Van An (1)
    Nguyen Van Dung (2)
    Zoran Kadelburg (3)
    Stojan Radenovi膰 (4)

    1. Department of Mathematics     ; Vinh University ; Vinh ; Nghe An ; Viet Nam
    2. Faculty of Mathematics and Information Technology Teacher Education     ; Dong Thap University ; Cao Lanh ; Dong Thap聽 ; 871200 ; Viet Nam
    3. Faculty of Mathematics     ; University of Belgrade ; Studentski trg 16 ; 11000聽 ; Beograd ; Serbia
    4. Faculty of Mechanical Engineering     ; University of Belgrade ; Kraljice Marije 16 ; 11120聽 ; Beograd ; Serbia
  • 关键词：Fixed point ; Metric space ; Generalized metric space ; Primary 47H10 ; 54H25 ; Secondary 54D99 ; 54E99
  • 刊名：Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
  • 出版年：2015
  • 出版时间：March 2015
  • 年：2015
  • 卷：109
  • 期：1
  • 页码：175-198
  • 全文大小：294 KB
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  • 刊物类别：Mathematics and Statistics
  • 出版者：Springer Milan
  • ISSN：1579-1505
文摘
There have been many attempts to generalize the definition of a metric space in order to obtain possibilities for more general fixed point results. In this paper, we give a survey of recent results on reducing fixed point theorems on generalized metric spaces to fixed point theorems on metric spaces and then investigate this fact in other generalized metric spaces. We show that many generalized metric spaces are topologically equivalent to certain metric spaces or to previously generalized metric spaces. Also, the fixed point theory in these generalized metric spaces may be a consequence of the fixed point theory in certain metric spaces or in previously generalized metric spaces.

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