Very recently, Shahzad et al. [RACSAM 111 (2017) 307–324] introduced the notion of (A, S)-contractions which unifies several well known nonlinear type contractions (e.g. R-contractions, Z-contractions, L-contractions etc.) in one go. In this paper, we introduce the notion of generalized (A, S) f-contractions and utilize the same to present some coincidence and common fixed point results for a pair of self-mappings (, f) defined on a metric space endowed with a binary relation S. In this course, we ought to introduce some new notions namely: (I, S)-continuity, (I, S)-compatibility and local (, f)-transitivity. Consequently, several results involving R-contractions and Z-contractions are deduced. Finally, we furnish illustrative examples to demonstrate the utility of our results.