Coupled fixed point theorems via mixed monotone property in $A_b$-metric spaces & applications to integral equations

In this paper, we establish some results on the existence and uniqueness of coupled common fixed point theorems in partially ordered $A_b$-metric spaces. Examples have been provided to justify the relevance of the results obtained through the analysis of extant theorem. Further, we also find application to integral equations via fixed point theorems in $A_b$-metric spaces.