zbMATH — the first resource for mathematics

Comments on ‘A common fixed point theorem in a fuzzy metric space’. (English) Zbl 1020.54009
M. Grabiec [ibid. 27, 385-389 (1988; Zbl 0664.54032)] proved a fuzzy Banach contraction theorem and R. Vasuki [ibid. 97, 395-397 (1998; Zbl 0926.54005)] generalized the results to a common fixed point theorem for a sequence of mappings in a fuzzy metric space.
The author points out some errors in the papers above; he claims that some conditions are indequate and the proofs are false.

54A40 Fuzzy topology
54H25 Fixed-point and coincidence theorems (topological aspects)
54E35 Metric spaces, metrizability
Full Text: DOI
[1] George, A.; Veeramani, P., On some results in fuzzy metric spaces, Fuzzy sets and systems, 64, 395-399, (1994) · Zbl 0843.54014
[2] Grebiec, M., Fixed point in fuzzy metric spaces, Fuzzy sets and systems, 27, 385-389, (1988)
[3] Schweizer, B.; Sklar, A., Statistical metric spaces, Pacific J. math., 10, 314-334, (1960) · Zbl 0091.29801
[4] Schweizer, B.; Sklar, A., Probabilistic metric spaces, (1983), North-Holland Amsterdam · Zbl 0546.60010
[5] Vasuki, R., A common fixed point theorem in a fuzzy metric space, Fuzzy sets and systems, 97, 395-397, (1998) · Zbl 0926.54005
[6] Zadeh, L.A., Fuzzy sets, Inform. control, 89, 338-353, (1965) · Zbl 0139.24606
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.