The authors discuss the following three topics:
Firstly, they slightly modify the implicit relation of the first author so that contraction conditions obtaining functional inequalities can be covered.
Secondly, using this modified implicit relation and weak compatibility, some common fixed point theorems are covered in 2-metric spaces and then their analog in metric spaces is discussed.
Finally, as an application of the main result, a Bryant type generalized common fixed point theorem is derived. Examples are given.