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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241–251 (1976)
S.S. Chang, Q. Luo, Set-valued Caristi’s fixed point theorem and Ekeland’s variational principle. Appl. Math. Mech. 10, 119–121 (1989)
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)
D. Downing, W.A. Kirk, A generalization of Caristi’s theorem with applications to nonlinear mapping theory. Pac. J. Math. 69, 339–346 (1977)
D. Dubois, H. Prade, Gradual elements in a fuzzy set. Soft. Comput. 12, 165–175 (2008)
I. Ekeland, On the variational principle. J. Math. Anal. Appl. 47, 324–353 (1974)
I. Ekeland, Nonconvex minimization problems. Bull. Am. Math. Soc. 1, 443–474 (1979)
J.X. Fang, On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 46, 107–113 (1992)
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, An improved completion theorem of fuzzy metric spaces. Fuzzy Sets Syst. 166, 65–74 (2011)
O. Hadžíc, Fixed point theorems for multi-valued mappings in some classes of fuzzy metric spaces. Fuzzy Sets Syst. 29, 115–125 (1989)
P.J. He, The variational principle in fuzzy metric spaces and its applications. Fuzzy Sets Syst. 45, 389–394 (1992)
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)
O. Kaleva, S. Seikkala, On fuzzy metric spaces. Fuzzy Sets Syst. 12, 215–229 (1984)
N. Mizoguchi, W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric spaces. J. Math. Anal. Appl. 141, 177–188 (1989)
S. Park, On extensions of the Caristi-Kirk fixed point theorem. J. Korean Math. Soc. 19, 143–151 (1983)
B. Schweizer, A. Sklar, Statistical metric spaces. Pac. J. Math. 10, 313–334 (1960)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Cho, Y.J., Rassias, T.M., Saadati, R. (2018). Coincidence Points for Set-Valued Mappings in Fuzzy Metric Spaces. In: Fuzzy Operator Theory in Mathematical Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-93501-0_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-93501-0_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93499-0
Online ISBN: 978-3-319-93501-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)