Meir-Keeler theorems in fuzzy metric spaces. (English) Zbl 1423.54029
Summary: In this paper, we propose the concept of fuzzy Meir-Keeler contractive mappings in fuzzy metric spaces, which covers fuzzy \(\psi\)-contractive mappings and fuzzy \(\mathcal{H}\)-contractive mappings as special cases. With the aid of the proposed concept, we obtain some Meir-Keeler type fixed point theorems. The derived theorems improve and extend the corresponding ones developed by D. Mihet, D. Wardowski [Fuzzy Sets Syst. 222, 108–114 (2013; Zbl 1284.54019)] and V. Gregori, et al. An example in the end of the paper illustrates the validity of our results.
MSC:
| 54A40 | Fuzzy topology |
| 54E15 | Uniform structures and generalizations |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
Keywords:
fuzzy metric space; fuzzy Meir-Keeler contractive mapping; fuzzy \(\psi\)-contractive mapping; fixed pointCitations:
Zbl 1284.54019References:
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