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Fixed point theorems for fuzzy \(\psi\)-contractive mappings in fuzzy metric spaces. (English) Zbl 1308.54039

Summary: D. Miheţ [Fuzzy Sets Syst. 159, No. 6, 739–744 (2008; Zbl 1171.54330); erratum ibid. 161, No. 8, 1150–1151 (2010)] proved a fixed point theorem for fuzzy \(\psi\)-contractive mappings in non-Archimedean fuzzy metric spaces. Motivated by this, in this paper, we provide two kinds of fixed point theorems in fuzzy metric spaces. First we prove a common fixed point theorem for fuzzy \(\psi\)-contractive mappings in fuzzy metric spaces and then we obtain a common fixed point theorem for three mappings in fuzzy metric spaces, by contractivity condition [D. Miheţ, Fuzzy Sets Syst. 144, No. 3, 431–439 (2004; Zbl 1052.54010)], [V. Radu, “Some remarks on the probabilistic on fuzzy menger spaces”, Automat. Comput. Appl. Math. 11, 125–131 (2002)].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54A40 Fuzzy topology
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