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Equivalents of the variational principle in fuzzy and probabilistic metric spaces. (English) Zbl 0946.54023
The authors investigate the variational principle in fuzzy metric spaces and prove some equivalents to it. They prove some fixed-point-type theorems for single- and multi-valued mappings. The obtained results are applied in probabilistic metric spaces of Menger type.
MSC:
54E70 Probabilistic metric spaces
54A40 Fuzzy topology
49J40 Variational inequalities
54H25 Fixed-point and coincidence theorems (topological aspects)
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