A Note on Various Classes of Compatible-Type Pairs of Mappings and Common Fixed Point Theorems

Table 1

If	Properties that trivially hold	Properties that cannot hold
𝐶(𝐴,𝑆)=∅	(7), (9), (19)	(8), (14), (15), (16), (17), (20)
ℒ(𝐴,𝑆)=∅	(3), (6), (11), (13), (18); (7), (9), (10), (19)	(2), (4), (5), (12); (8), (14), (15), (16), (17), (20)
𝐶(𝐴,𝑆)≠∅	(7) ⇒ (8), (8) ⇔ (9), (10) ⇒ (8); (8) ⇒ (17), (19) ⇒ (20); (2), (3) ⇒ (6), (5) ⇔ (6); (11) ⇒ (12), (12) ⇔ (13)
ℒ(𝐴,𝑆)≠∅	(2), (3) ⇒ (6), (5) ⇔ (6); (11) ⇒ (12), (12) ⇔ (13)