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

Abstract

[EN] We obtain a fixed point theorem for complete fuzzy metric spaces, in the sense of Kramosiland Michalek, that extends the classical Kannan fixed point theorem. We also show that, in fact, ourtheorem 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 afixed point.