## An extension of Ekeland’s variational principle in fuzzy metric space and its applications.(English)Zbl 0946.49017

Authors’ summary: “An extension of Ekeland’s variational principle in fuzzy metric space, which is an essential and the most general improvement of Ekeland’s variational principle in fuzzy metric space up to now, is established. As an application, we obtain Caristi’s coincidence theorem for set-valued mappings in fuzzy metric space. Further, a direct simple proof of the equivalence between the two theorems is given. Some applications of these results to probabilistic metric spaces are presented. All these results, even in usual metric spaces, are also new”.

### MSC:

 49K27 Optimality conditions for problems in abstract spaces 54A40 Fuzzy topology 54H25 Fixed-point and coincidence theorems (topological aspects)
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