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Zbl 0986.54016
Jung, J.S.; Chang, S.S.; Cho, Y.J.; Lee, B.S.; Kang, S.M.
Common fixed point theorems and variational principle in generating spaces of quasi-metric family. (English)
[J] Fuzzy Sets Syst. 102, No.2, 315-325 (1999). ISSN 0165-0114

Summary: We introduce the concept of order relation in generating spaces of quasi-metric family and establish common-fixed-point theorems for set-valued mappings in this spaces. As consequences, we also give a variational principle, fixed point theorems for single-valued and set-valued mappings and equivalence between them in complete generating spaces of quasi-metric family. Some applications of these results to fuzzy metric spaces in the sense of {\it O. Kaleva} and {\it S. Seikkala} [ibid. 12, 215-229 (1984; Zbl 0558.54003)] and to probabilistic metric spaces are presented.

MSC 2000:: *54A40 Fuzzy topology
54H25 Fixed-point theorems in topological spaces
54C60 Set-valued maps
58E35 Variational inequalities (global problems)
49J40 Variational methods including variational inequalities

Keywords: variational principle; fuzzy metric spaces; probabilistic metric spaces

Citations: Zbl 0558.54003

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