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Topologies and Fixed Points in Fuzzy Metric-Type Spaces

  • Yeol Je Cho
  • Themistocles M. Rassias
  • Reza Saadati
Chapter

Abstract

In this chapter, first, we introduce some extensions of metric spaces. Next, we introduce the concept of fuzzy metric-type spaces and consider the topology induced by the fuzzy metric type. Finally, we consider some fixed point theorems for some nonlinear mapping satisfying some conditions in complete fuzzy metric-type spaces.

References

  1. 7.
    M.A. Alghamdi, N. Hussain, P. Salimi, Fixed point and coupled fixed point theorems on b-metric-like spaces. J. Inequal. Appl. 2013, Article ID 402 (2013)MathSciNetCrossRefGoogle Scholar
  2. 12.
    A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points. Fixed Point Theory Appl. 2012, Article ID 204 (2012)MathSciNetCrossRefGoogle Scholar
  3. 15.
    M. Asadi, E. Karapinar, P. Salimi, New extension of p-metric spaces with some fixed-point results on M-metric spaces. J. Inequal. Appl. 2014, 18 (2014)MathSciNetCrossRefGoogle Scholar
  4. 19.
    I.A. Bakhtin, The contraction mapping principle in almost metric spaces, in Functional Analysis, vol. 30 (Ul’yanovsk Gos. Ped. Inst., Ul’yanovsk, 1989), pp. 26–37Google Scholar
  5. 103.
    S. Matthews, Partial metric topology. Ann. N.Y. Acad. Sci. 728, 183–197 (1994)Google Scholar
  6. 117.
    D. O’Regan, R. Saadati, Nonlinear contraction theorems in probabilistic spaces. Appl. Math. Comput. 195, 86–93 (2008)MathSciNetMATHGoogle Scholar
  7. 151.
    C. Zhu, C. Chen, X. Zhang, Some results in quasi-b-metric-like spaces. J. Inequal. Appl. 2014, 437 (2014)MathSciNetCrossRefGoogle Scholar
  8. 152.
    L. Zhu, C.X. Zhu, C.F. Chen, Z. Stojanović, Multidimensional fixed points for generalized ψ-quasi-contractions in quasi-metric-like spaces. J. Inequal. Appl. 2014, Article ID 27 (2014)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Yeol Je Cho
    • 1
    • 2
  • Themistocles M. Rassias
    • 3
  • Reza Saadati
    • 4
  1. 1.Department of Mathematical EducationGyeongsang National UniversityJinjuKorea (Republic of)
  2. 2.School of Mathematical ScienceUniversity of Electronic Science and Technology of ChinaChengduChina
  3. 3.Department of MathematicsNational Technical University of AthensAthensGreece
  4. 4.Department of MathematicsIran University of Science and TechnologyTehranIran

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