Fixed point results for generalized (ψ,ϕ)-weak contractions with an application to system of non-linear integral equations

The aim of this paper is to prove fixed point results under $(\psi ,\varphi )$-weak contractive condition for continuous weak compatible mappings in ordered $b$-metric spaces. The results proved herein generalize, modify and unify some recent results of the existing literature. An application demonstrating the usability of our established results is also discussed besides furnishing an illustrative example.