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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.

MSC:
54A40 Fuzzy topology
54H25 Fixed-point and coincidence theorems (topological aspects)
54E35 Metric spaces, metrizability
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[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
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