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

✍ Scribed by Jiang Zhu; Cheng-kui Zhong; Ge-ping Wang

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 125 KB
• Volume: 108
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(97)00333-3

✦ Synopsis

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 spaces. 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 space, are also the latest.