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Zbl 0880.47030
Chang, Sh.; Cho, Y.J.; Kim, J.K.
Ekeland's variational principle and Caristi's coincidence theorem for set-valued mappings in probabilistic metric spaces.
(English)
[J] Period. Math. Hung. 33, No.2, 83-92 (1996). ISSN 0031-5303; ISSN 1588-2829/e

The authors prove a common generalization of {\it I. Ekeland's} variational principle [Bull. Am. Math. Soc., New Ser. 1, 443-474 (1979; Zbl 0441.49011)] and {\it J. Caristi's} coincidence theorem [Trans. Am. Math. Soc. 215, 241-251 (1976; Zbl 0305.47029)] for set-valued mappings in probabilistic metric spaces. They also give a direct proof of the equivalence of these two theorems in probabilistic metric spaces, generalizing a previous result of {\it S.Z. Shi} [Advan. Math., Beijing, 16, 203-206 (1987; Zbl 0621.54030)].
[J.Appell (Würzburg)]
MSC 2000:
*47H04 Set-valued operators
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
60B99 Probability theory on general structures
49R50 Variational methods for eigenvalues of operators

Keywords: distribution function; $t$-norm; a Menger PM-space; Caristi's coincidence theorem; Ekeland's variational principle

Citations: Zbl 0441.49011; Zbl 0305.47029; Zbl 0621.54030

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