Abstract
F-contractions have inspired a branch of metric fixed point theory committed to the generalization of the classical Banach contraction principle. The study of these contractions and α-fuzzy mappings in b-metric spaces was attempted timidly and was not successful. In this article, the main objective is to obtain common α-fuzzy fixed point results for F-contractions in b-metric spaces. Some multivalued fixed point results in the literature are derived as consequences of our main results. We also provide a non-trivial example to show the validity of our results. As applications, we investigate the solution for fuzzy initial value problems in the context of a generalized Hukuhara derivative. Our results generalize, improve and complement several developments from the existing literature.
Highlights
Zadeh [1] introduced the notion of fuzzy set as a means of dealing with unpredictability that is induced due to inaccuracy or obscurity in preference to haphazardness in 1960
Ali et al [23,24] used the notion of β-admissible mappings and Fcontractions to obtain Feng and Liu type fixed point results in the context of b-metric space
We establish some common α-fuzzy fixed point theorems for β-admissible mappings and F-contractions in the setting of complete b-metric space to generalize the main results of Ahmad et al [7], Wardowski [18] and Cosentino et al [22] and some familiar theorems of the literature
Summary
Zadeh [1] introduced the notion of fuzzy set as a means of dealing with unpredictability that is induced due to inaccuracy or obscurity in preference to haphazardness in 1960. Estruch et al [3] established the existence of a fuzzy fixed point for fuzzy contraction mappings in the context of complete metric space. Ali et al [23,24] used the notion of β-admissible mappings and Fcontractions to obtain Feng and Liu type fixed point results in the context of b-metric space. We establish some common α-fuzzy fixed point theorems for β-admissible mappings and F-contractions in the setting of complete b-metric space to generalize the main results of Ahmad et al [7], Wardowski [18] and Cosentino et al [22] and some familiar theorems of the literature
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