### A fixed point theorem of Kannan type that characterizes fuzzy metric completeness

#### Abstract

We obtain a fixed point theorem for complete fuzzy metric spaces, in the

sense of Kramosil and Michalek, that extendes the classical Kannan fixed

point theorem. We also show that, in fact, our theorem allows to

characterize the fuzzy metric completeness, extending in this way the

well-known Reich-Subrahmanyam theorem that a metric space is complete if and only if every Kannan contraction on it has a fixed point.

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