Several authors have introduced various conditions which can be used in order to prove common fixed point results. However, it became clear recently that some of these conditions, though formally distinct from each other, actually coincide in the case when the given mappings have a unique point of coincidence. Hence, in fact, new common fixed point results cannot be obtained in this way. We make a review of such connections and results in this paper.
"A Note on Various Classes of Compatible-Type Pairs of Mappings and Common Fixed Point Theorems." Abstr. Appl. Anal. 2013 (SI09) 1 - 6, 2013. https://doi.org/10.1155/2013/697151