Vector-valued variational principle in fuzzy metric space and its applications

A vector-valued Ekeland's variational principle and its equivalents in fuzzy metric space are presented in this paper. Our result unifies and extends some of the previous results about single-valued and vector-valued Ekeland's variational principle. As an application, we obtain a fixed-point theorem in fuzzy metric space under a new contractive condition, which is a new generalization of well-known Banach contraction principle. All of our results are also new even in usual metric spaces.

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