Skip to main content
Top

2018 | OriginalPaper | Chapter

13. Coincidence Points for Set-Valued Mappings in Fuzzy Metric Spaces

Authors : Yeol Je Cho, Themistocles M. Rassias, Reza Saadati

Published in: Fuzzy Operator Theory in Mathematical Analysis

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this chapter, we prove some coincidence theorem for set-valued mappings in fuzzy metric spaces with a view to generalizing Downing-Kirk’s fixed point theorem in metric spaces.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
29.
go back to reference J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241–251 (1976)MathSciNetCrossRef J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241–251 (1976)MathSciNetCrossRef
31.
go back to reference S.S. Chang, Q. Luo, Set-valued Caristi’s fixed point theorem and Ekeland’s variational principle. Appl. Math. Mech. 10, 119–121 (1989)MathSciNetCrossRef S.S. Chang, Q. Luo, Set-valued Caristi’s fixed point theorem and Ekeland’s variational principle. Appl. Math. Mech. 10, 119–121 (1989)MathSciNetCrossRef
33.
go back to reference S.S. Chang, Y.J. Cho, B.S. Lee, J.S. Jung, S.M. Kang, Coincidence point theorems and minimization theorems in fuzzy metric spaces. Fuzzy Sets Syst. 88, 119–127 (1997)MathSciNetCrossRef S.S. Chang, Y.J. Cho, B.S. Lee, J.S. Jung, S.M. Kang, Coincidence point theorems and minimization theorems in fuzzy metric spaces. Fuzzy Sets Syst. 88, 119–127 (1997)MathSciNetCrossRef
42.
go back to reference D. Downing, W.A. Kirk, A generalization of Caristi’s theorem with applications to nonlinear mapping theory. Pac. J. Math. 69, 339–346 (1977)MathSciNetCrossRef D. Downing, W.A. Kirk, A generalization of Caristi’s theorem with applications to nonlinear mapping theory. Pac. J. Math. 69, 339–346 (1977)MathSciNetCrossRef
43.
go back to reference D. Dubois, H. Prade, Gradual elements in a fuzzy set. Soft. Comput. 12, 165–175 (2008)CrossRef D. Dubois, H. Prade, Gradual elements in a fuzzy set. Soft. Comput. 12, 165–175 (2008)CrossRef
48.
go back to reference J.X. Fang, On the generalization of Ekeland’s variational principle and Caristi’s fixed point theorem, in The 6th National Conference on the Fixed Point Theory, Variational Inequalities and Probabilistic Metric Space Theory, Qingdao (1993) J.X. Fang, On the generalization of Ekeland’s variational principle and Caristi’s fixed point theorem, in The 6th National Conference on the Fixed Point Theory, Variational Inequalities and Probabilistic Metric Space Theory, Qingdao (1993)
65.
go back to reference O. Hadžíc, Fixed point theorems for multi-valued mappings in some classes of fuzzy metric spaces. Fuzzy Sets Syst. 29, 115–125 (1989)CrossRef O. Hadžíc, Fixed point theorems for multi-valued mappings in some classes of fuzzy metric spaces. Fuzzy Sets Syst. 29, 115–125 (1989)CrossRef
72.
go back to reference P.J. He, The variational principle in fuzzy metric spaces and its applications. Fuzzy Sets Syst. 45, 389–394 (1992)MathSciNetCrossRef P.J. He, The variational principle in fuzzy metric spaces and its applications. Fuzzy Sets Syst. 45, 389–394 (1992)MathSciNetCrossRef
83.
go back to reference J.S. Jung, Y.J. Cho, J.K. Kim, Minimization theorems for fixed point theorems in fuzzy metric spaces and applications. Fuzzy Sets Syst. 61, 199–207 (1994)MathSciNetCrossRef J.S. Jung, Y.J. Cho, J.K. Kim, Minimization theorems for fixed point theorems in fuzzy metric spaces and applications. Fuzzy Sets Syst. 61, 199–207 (1994)MathSciNetCrossRef
86.
go back to reference O. Kaleva, S. Seikkala, On fuzzy metric spaces. Fuzzy Sets Syst. 12, 215–229 (1984)CrossRef O. Kaleva, S. Seikkala, On fuzzy metric spaces. Fuzzy Sets Syst. 12, 215–229 (1984)CrossRef
114.
go back to reference N. Mizoguchi, W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric spaces. J. Math. Anal. Appl. 141, 177–188 (1989)MathSciNetCrossRef N. Mizoguchi, W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric spaces. J. Math. Anal. Appl. 141, 177–188 (1989)MathSciNetCrossRef
118.
Metadata
Title
Coincidence Points for Set-Valued Mappings in Fuzzy Metric Spaces
Authors
Yeol Je Cho
Themistocles M. Rassias
Reza Saadati
Copyright Year
2018
DOI
https://doi.org/10.1007/978-3-319-93501-0_13

Premium Partner