Common fixed point theorems for compatible and weakly compatible maps in fuzzy cone metric spaces

Journal of Function Spaces

Yazbek

Bantan

et al. 2021

This paper is aimed at proving some unique common fixed point theorems by using the compatible and weakly-compatible four self-mappings in fuzzy cone metric (FCM) space. We prove the results under the generalized rational contraction conditions in FCM spaces with the help of one self-map are continuous. Furthermore, we prove some rational contraction results with the weaker condition of the self-mapping continuity. Ultimately, our theoretical work has been utilized to prove the existence solution of the two nonlinear integral equations. This is an illustrative application of how FCM spaces can be used in other integral type operators.

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Some Compatible and Weakly-Compatible Four Self-Mapping Results Approach to Nonlinear Integral Equations in Fuzzy Cone Metric Spaces

Journal of Function Spaces

Yazbek

Bantan

et al. 2021

Some $α - ϕ$ -Fuzzy Cone Contraction Results with Integral Type Application

Jabeen

Khan

et al. 2021

Journal of Mathematics

In this paper, we define α -admissible and α - ϕ -fuzzy cone contraction in fuzzy cone metric space to prove some fixed point theorems. Some related sequences with contraction mappings have been discussed. Ultimately, our theoretical results have been utilized to show the existence of the solution to a nonlinear integral equation. This application is also illustrative of how fuzzy metric spaces can be used in other integral type operators.

Rational Fuzzy Cone Contractions on Fuzzy Cone Metric Spaces with an Application to Fredholm Integral Equations

Journal of Function Spaces

Aydi

2021

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 .