Abstract
In the present research, modern fuzzy technique is used to generalize some conventional and latest results. The objective of this paper is to construct and prove some fixed-point results in complete fuzzy strong b-metric space. Fuzzy strong b-metric (sb-metric) spaces have very useful properties such as openness of open balls whereas it is not held in general for b-metric and fuzzy b-metric spaces. Due to its properties, we have worked in these spaces. In this way, we have generalized some well-known fixed-point theorems in fuzzy version. In addition, some interesting examples are constructed to illustrate our results.
Highlights
In pure mathematics, the theory of fixed points is the most dynamic and active area of research. e theory of fixed points has already been revealed as a great and significant weapon for studying nonlinear analysis
Strong b-metric space has the advantage over b-metric spaces that, in the induced topology, open balls are open, so they stake a number of characteristics that are the same to those of classic metric space
Integral equations arise in several problems in mathematical physics, control theory, critical point theory for nonsmooth energy functionals, differentials, variational inequalities, fuzzy set arithmetic, traffic theory, etc. ese can be solved by fixed-point methods
Summary
The theory of fixed points is the most dynamic and active area of research. e theory of fixed points has already been revealed as a great and significant weapon for studying nonlinear analysis. Is work lays a solid foundation for the expansion of fixed-point theory in fuzzy metric space. Fang [17] further sets some latest fixed-point theorems for contractive-type mappings in G-complete fuzzy metric space by following Grabiec’s work. Open balls may not be open, closed balls may not be closed, and a b-metric may not be continuous as a mapping in the induced topology. Strong b-metric space has the advantage over b-metric spaces that, in the induced topology, open balls are open, so they stake a number of characteristics that are the same to those of classic metric space. In 2019, Oner and Sostak [22] have introduced the definition and properties of strong fuzzy b-metric space. E aim of the present paper is to go further in the research of fuzzy sbmetric spaces.
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