Some results related to Caristi's fixed point theorem and Ekeland's variational principle

• Autorzy: Pathak H. , Mishra S.
• Języki publikacji: EN

Słowa kluczowe

EN

coincidence theorems; variational principle; fuzzy metric spaces

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 4
• Strony: 859--872
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Pathak H.

• Department of Mathematics, Kalyan Mahavidyalaya Bhilainagar 4990006 (M.P.), India

autor

Mishra S.

• Departament of Mathematics, University of Transkei Umtata 5100, South Africa

Bibliografia

• [1] E. Bishop and R. Phelps, The support functional of a convex set, in "Convexity" (Klee, Ed.), Proc. Symp. Pure Math. Vol. 7, 27-35, Amer. Math. Soc., Providence, RI, 1963.
• [2] A. Brøndsted, On a lemma of Bishop and Phelps, Pacific J. Math. 55 (1974), 335-341.
• [3] J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc. 215 (1976) 241-251.
• [4] S. S. Chang and Q. Luo, Set-valued Caristi's fixed point theorem and Ekeland's variational principle, Appl. Math, and Mech. 10 (1989) 119-121.
• [5] 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.
• [6] I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974) 324-353.
• [7] I. Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc. (New Series) 1 (1979) 443-474.
• [8] J. X. Fang, A note on fixed point theorems of Hadzic, Fuzzy Sets and Systems 48 (1991) 391-395.
• [9] O. Hadzic, Fixed point theorems for multi-valued mappings in some classes of fuzzy metric spaces, Fuzzy Sets and Systems 29 (1989) 115-125.
• [10] P. J. He, The variational principle in fuzzy metric spaces and its applications, Fuzzy Sets and Systems 45 (1992) 289-394.
• [11] J. S. Jung, Y. J. Cho, S. M. Kang and S. S. Chang, Coincidence theorems for set-valued mappings and Ekeland's variational principle in fuzzy metric spaces, Fuzzy Sets and Systems 79 (1996), 239-250.
• [12] 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.
• [13] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems 12 (1984) 215-229.
• [14] W. A. Kirk, Caristi's fixed point theorem and the theory of normal solvability, Seminar on Fixed Point Theory and its Applications, Dalhousie University, 1975.
• [15] W. A. Kirk and J. Caisti, Mapping theorems in metric and Banach spaces, Bull. Acad. Polon. Sci. 32 (1975), 891-894.
• [16] N. Mizoguchi and W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177-188.
• [17] S. Park, On extensions of the Caristi-Kirk fixed point theorem, J. Korean Math. Soc. 19 (1983) 143-151.
• [18] B. Schweizer and A. Sklar, Satstical metric spaces, Pacific J. Math. 10 (1960) 313-334.