A New Fixed Point Theorem for Generalized \((α, ψ)\)-Contraction Mapping of Quadratic Type With Applications - Tiwari, Rakesh; Sharma, Nidhi (Communications in Mathematics and Applications, 2024)
In this paper, we acquaint generalized \((α,ψ)\)-contraction mappings of quadratic type and establish common fixed point results in the setting of rectangular quasi \(b\)-metric spaces. Our results extend and generalize related fixed point results of Karapinar and Lakzian \((α-ψ)\)-Contractive mappings on generalized quasi metric spaces, Journal of Function Spaces 2014 (2014), 914398, 7 pages), Alharbi et al.~(\(α\)-Contractive mappings on rectangular \(b\)-metric spaces and an application to integral equations, Journal of Mathematical Analysis 9(3) (2018), 47 - 60), and Khuangsatung et al. (The rectangular quasi-metric space and common fixed point theorem for \(ψ\)-contraction and \(ψ\)-Kannan mappings, Thai Journal of Mathematics (Special Issue (2020): Annual Meeting in Mathematics 2019), (2020), 89 - 101). We applied our result to facilitate the existence of a solution to an integral equation.