In this paper, among other things, we have established four different types of compatible mappings that work in the context of C*-algebra valued metric spaces. The obtained types of mappings generalize from previously known ones within ordinary metric spaces. We have shown by examples that these types of mappings are really different. They can be used to consider new fixed point results which were done in the paper for the case of common fixed points of some mappings. The results in this paper generalize, extend, unify, enrich and complement many known results in the existing literature.