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A new class of fuzzy contractive mappings and fixed point theorems. (English) Zbl 1397.54057

Summary: The main aim of this work is to unify different classes of fuzzy contractive mappings by introducing a new class of fuzzy contractive mappings called fuzzy \(\mathcal{Z}\)-contractive mappings. For this new class of mappings, suitable conditions are framed to ensure the existence of fixed point in \(M\)-complete fuzzy metric spaces (in the sense of A. George and P. Veeramani [ibid. 64, No. 3, 395–399 (1994; Zbl 0843.54014)]). A comprehensive set of examples are presented to support the claim.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54A40 Fuzzy topology

Citations:

Zbl 0843.54014
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Full Text: DOI

References:

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