{\(\alpha\)}-type fuzzy \(H\)-contractive mappings in fuzzy metric spaces. (English) Zbl 1460.54037
Summary: We introduce a new concept of {\(\alpha\)}-fuzzy \(\mathcal{H}\)-contractive mapping which is essentially weaker than the class of fuzzy contractive mapping and stronger than the concept of {\(\alpha\)}-{\(\phi\)}-fuzzy contractive mapping. For this type of contractions, the existence and uniqueness of fixed point in fuzzy \(M\)-complete metric spaces is also established.
MSC:
54H25 | Fixed-point and coincidence theorems (topological aspects) |
54A40 | Fuzzy topology |
54E40 | Special maps on metric spaces |
54E50 | Complete metric spaces |