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.