Kybernetika 57 no. 6, 908-921, 2021

Suzuki type fuzzy Z-contractive mappings and fixed points in fuzzy metric spaces

Dhananjay Gopal and Juan Martínez-MorenoDOI: 10.14736/kyb-2021-6-0908

Abstract:

In this paper, we propose the concept of Suzuki type fuzzy $\mathcal{Z}$-contractive mappings, which is a generalization of Fuzzy $\mathcal{Z}$-contractive mappings initiated in the article [S. Shukla, D. Gopal, W. Sintunavarat, A new class of fuzzy contractive mappings and fixed point theorems, Fuzzy Sets and Systems 350 (2018)85-95]. For this type of contractions suitable conditions are framed to ensure the existence of fixed point in $G$-complete as well as $M$-complete fuzzy metric spaces. A comprehensive set of examples are furnished to demonstrate the validity of the obtained results.

Keywords:

fuzzy metric space, fixed point, fuzzy $\mathcal {Z}$-contractive mapping, Suzuki type fuzzy $\mathcal {Z}$-contractive mappings

Classification:

54H25, 47H10

paper.pdf

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