Abstract
In this paper, we establish a Hausdorff metric over the family of nonempty closed subsets of an extended b -metric space. Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related α -fuzzy fixed point theorems in the context of extended b -metric spaces that generalize Nadler’s fixed point theorem as well as many preexisting results in the literature. Further, we establish α -fuzzy fixed point theorems for Ćirić type fuzzy contraction mappings as a generalization of previous results. Moreover, we give some examples to support the obtained results.
Highlights
In 1928, Von Neumann [1] introduced the concept of fixed points for multivalued mappings because of its applications in several branches of mathematics. e development of the geometric fixed point theory for multivalued mappings was initiated by the work of Nadler [2]
In 1981, Heilpern [4] proved a fixed point theorem for fuzzy contraction mappings as a generalization of Nadler’s contraction principle
In 2015, Phiangsungnoen and Kumam [12] established the concept of multivalued fuzzy contraction mappings in b-metric spaces and proved a related α-fuzzy fixed point theorem
Summary
In 1928, Von Neumann [1] introduced the concept of fixed points for multivalued mappings because of its applications in several branches of mathematics. e development of the geometric fixed point theory for multivalued mappings was initiated by the work of Nadler [2]. In 2015, Phiangsungnoen and Kumam [12] established the concept of multivalued fuzzy contraction mappings in b-metric spaces and proved a related α-fuzzy fixed point theorem. Kamran in [14] introduced the concept of an extended b-metric, as a generalization of a b-metric, and proved fixed point results on such space.
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