Abstract
This paper is aimed at proving some common fixed point theorems for mappings involving generalized rational-type fuzzy cone-contraction conditions in fuzzy cone metric spaces. Some illustrative examples are presented to support our work. Moreover, as an application, we ensure the existence of a common solution of the Fredholm integral equations: μ τ = ∫ 0 τ Γ τ , v , μ v d v and ν τ = ∫ 0 τ Γ τ , v , ν v d v , for all μ ∈ U , v ∈ 0 , η , and 0 < η ∈ ℝ , where U = C 0 , η , ℝ is the space of all ℝ -valued continuous functions on the interval 0 , η and Γ : 0 , η × 0 , η × ℝ ⟶ ℝ .
Highlights
In 1922, Banach [1] proved a “Banach contraction principle,” which is stated as follows: “A self-mapping on a complete metric space verifying the contraction condition has a unique fixed point.”
A number of researches have generalized it in many directions for single-valued and multivalued mappings in the context of metric spaces
We prove some common fixed point theorems via generalized rational-type fuzzy cone-contraction conditions in FCM spaces
Summary
In 1922, Banach [1] proved a “Banach contraction principle,” which is stated as follows: “A self-mapping on a complete metric space verifying the contraction condition has a unique fixed point.” This principle plays a very important role in the fixed point theory. In 1922, Banach [1] proved a “Banach contraction principle,” which is stated as follows: “A self-mapping on a complete metric space verifying the contraction condition has a unique fixed point.”. This principle plays a very important role in the fixed point theory. A number of researches have generalized it in many directions for single-valued and multivalued mappings in the context of metric spaces. The fixed point theory is one of the most interested research areas in the field of mathematics. It has been investigated in many fields, such as game theory, graph theory, economics, computer sciences, and engineering
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