Open AccessA fixed point theorem of Kannan type that characterizes fuzzy metric completeness
Author(s) -
Salvador Romaguera
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2014811r
Subject(s) - mathematics , fixed point theorem , metric space , kakutani fixed point theorem , completeness (order theory) , brouwer fixed point theorem , fixed point property , discrete mathematics , fixed point , complete metric space , contraction mapping , injective metric space , least fixed point , pure mathematics , schauder fixed point theorem , mathematical analysis
We obtain a fixed point theorem for complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends 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.