# A New Fixed Point Theorem for Generalized \((\alpha, \psi)\)-Contraction Mapping of Quadratic Type With~Applications

## DOI:

https://doi.org/10.26713/cma.v15i1.2557## Keywords:

Fixed point, \((\alpha, \psi)\)-contraction, \(b\)-metric space## Abstract

In this paper, we acquaint generalized \((\alpha,\psi)\)-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 \((\alpha-\psi)\)-Contractive mappings on generalized quasi metric spaces, *Journal of Function Spaces * **2014** (2014), 914398, 7 pages), Alharbi *et al*.~(\(\alpha\)-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 \(\psi\)-contraction and \(\psi\)-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.

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*Communications in Mathematics and Applications*,

*15*(1), 445–461. https://doi.org/10.26713/cma.v15i1.2557

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