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Comment on: “Common fixed point theorems for commutating mappings in fuzzy metric spaces”. (English) Zbl 1256.54082
Summary: In a recent paper [ibid. 2012, Article ID 729758, 5 p. (2012; Zbl 1242.54032)], {\it F. Zheng} and {\it X. Lian} proved a common fixed-point theorem for commutating mappings in $G$-complete fuzzy metric spaces and gave an example to illustrate the main result. In this note, we point out that the above example is incorrect because it does not satisfy the condition of $G$-completeness, and then two appropriate examples are given. In addition, we prove that the theorem proposed in [loc. cit.] actually holds in an $M$-complete fuzzy metric space. Our results improve and extend some existing results in the relevant literature.

54H25Fixed-point and coincidence theorems in topological spaces
54A40Fuzzy topology
Full Text: DOI
[1] F. M. Zheng and X. G. Lian, “Common fixed point theorems for commutating mappings in fuzzy metric spaces,” Abstract and Applied Analysis, vol. 2012, Article ID 729758, 5 pages, 2012. · Zbl 1242.54032
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