Various generalizations of metric spaces and fixed point theorems

  • Tran Van An
  • Nguyen Van Dung
  • Zoran Kadelburg
  • Stojan Radenović
Original Paper

DOI: 10.1007/s13398-014-0173-7

Cite this article as:
Van An, T., Van Dung, N., Kadelburg, Z. et al. RACSAM (2015) 109: 175. doi:10.1007/s13398-014-0173-7

Abstract

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.

Keywords

Fixed point Metric space Generalized metric space 

Mathematics Subject Classification (2010)

Primary 47H10 54H25 Secondary 54D99 54E99 

Copyright information

© Springer-Verlag Italia 2014

Authors and Affiliations

  • Tran Van An
    • 1
  • Nguyen Van Dung
    • 2
  • Zoran Kadelburg
    • 3
  • Stojan Radenović
    • 4
  1. 1.Department of MathematicsVinh UniversityVinhViet Nam
  2. 2.Faculty of Mathematics and Information Technology Teacher EducationDong Thap UniversityCao LanhViet Nam
  3. 3.Faculty of MathematicsUniversity of BelgradeBeogradSerbia
  4. 4.Faculty of Mechanical EngineeringUniversity of BelgradeBeogradSerbia

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