An extension of Ekeland's variational principle in fuzzy metric space and its applications

An extension of Ekeland's variational principle in fuzzy metric space, whic h is an essential and the most general improvement of Ekeland's variational principle in fuzzy metric space up to now, is established. As an applicati on, we obtain Caristi's coincidence theorem for set-valued mappings in fuzz y metric spaces. Further, a direct simple proof of the equivalence between the two theorems is given. Some applications of these results to probabilis tic metric spaces are presented. All these results, even in usual metric sp ace, are also the latest. (C) 1999 Elsevier Science B.V. All rights reserve d.