Abstract
The aim of this article is to establish some fixed point results for fuzzy mappings and derive some corresponding multivalued mappings results of literature. For this purpose, we define some new and generalized contractions in the setting of b-metric spaces. As applications, we find solutions of integral inclusions by our obtained results.
Highlights
Introduction and PreliminariesIn 1981, Heilpern [1] utilized the approach of fuzzy set to initiate a family of fuzzy mappings which are extensions of multivalued mappings and obtained a result for these mappings in metric linear space
A fuzzy set in M is a function with domain M and values in [0, 1], I M is the collection of all fuzzy sets in M
The purpose of this paper is to present some common α-fuzzy fixed points for fuzzy mappings via F-contraction in complete b-metric space to extend the main result of Heilpern [1], Wardowski [18], Ahmad et al [19], Sgroi et al [21], Cosentino et al [24] and Shahzad et al [27] and some known results of literature
Summary
In 1981, Heilpern [1] utilized the approach of fuzzy set to initiate a family of fuzzy mappings which are extensions of multivalued mappings and obtained a result for these mappings in metric linear space. A fuzzy set in M is a function with domain M and values in [0, 1], I M is the collection of all fuzzy sets in M. If Θ is a fuzzy set and μ ∈ M, the function values Θ(μ) is called the grade of membership of μ in Θ. The α -level set of A is denoted by [Θ]α and is defined as follows:. Θ denotes the closure of the set Θ. Let F (M) be the collection of all fuzzy sets in a metric space M
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