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

• Main Authors: Saif Ur Rehman, Hassen Aydi
• Format: Article
• Language: English
• Published: Hindawi Limited 2021-01-01
• Series: Journal of Function Spaces
• Online Access: http://dx.doi.org/10.1155/2021/5527864

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: μτ=∫0τΓτ,v,μvdv and ντ=∫0τΓτ,v,νvdv, for all μ∈U, v∈0,η, and 0<η∈ℝ, where U=C0,η,ℝ is the space of all ℝ-valued continuous functions on the interval 0,η and Γ:0,η×0,η×ℝ⟶ℝ.