Coincidence theorems for set-valued mappings and Ekeland's variational principle in fuzzy metric spaces

Fuzzy Sets and Systems

Volumn 79, Issue 2, 1996, Pages 239-250

  Jung, Jong Soo ^a   Cho, Yeol Je ^b   Kang, Shin Min ^b   Chang, Shih Sen ^c  

^a Dong A University   (South Korea)

^b Gyeongsang National University   (South Korea)

^c SICHUAN UNIVERSITY   (China)

Author keywords

Fixed point theorem; Fuzzy coincidence theorem; Fuzzy metric space; Fuzzy variational principle

Indexed keywords

COMPUTATION THEORY; CONFORMAL MAPPING; EQUIVALENCE CLASSES; PROBABILISTIC LOGICS; SET THEORY; THEOREM PROVING; VARIATIONAL TECHNIQUES;

COINCIDENCE THEOREMS; FIXED POINT THEOREM; FUZZY METRIC SPACE; SET VALUED MAPPINGS;

FUZZY SETS;

EID: 0030127797     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/0165-0114(95)00084-4     Document Type: Article

References (13)

1. J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc. 215 (1976) 241-251.
2. S.S. Chang and Q. Luo, Set-valued Caristi's fixed point theorem and Ekeland's variational principle, Appl. Math. Mech. 10 (1989) 119-121.
3. D. Downing and W.A. Kirk, A generalization of Caristi's theorem with applications to nonlinear mapping theory, Pacific J. Math. 69 (1977) 339-346.
4. I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974) 324-353.
5. I. Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc. (New Series) 1 (1979) 443-474.
6. J.X. Fang, A note on fixed point theorems of Hadžîc, Fuzzy Sets and Systems 48 (1991) 391-395.
7. O. Hadžíc, Fixed point theorems for multi-valued mappings in some classes of fuzzy metric spaces, Fuzzy Sets and Systems 29 (1989) 115-125.
8. P.J. He, The variational principle in fuzzy metric spaces and its applications, Fuzzy Sets and Systems 45 (1992) 389-394.
9. J.S. Jung, Y.J. Cho and J.K. Kim, Minimization theorems for fixed point theorems in fuzzy metric spaces and applications, Fuzzy Sets and Systems 61 (1994) 199-207.
10. O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems 12 (1984) 215-229.
11. N. Mizoguchi and W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal Appl. 141 (1989) 177-188.
12. S. Park, On extensions of the Caristi-Kirk fixed point theorem, J. Korean Math. Soc. 19 (1983) 143-151.
13. B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960) 313-334.