zbMATH — the first resource for mathematics

A note on occasionally weakly compatible maps. (English) Zbl 1181.54045
The authors introduced the concept of occasionally weakly compatible maps in [Acta Math. Sin., Engl. Ser. 24, No. 5, 867–876 (2008; Zbl 1175.41026)]. Here, they prove that a pair of selfmaps of a discrete metric space is weakly compatible iff it is weakly commuting, provided that the set of their coincidence points is nonempty. A suitable example shows that this remark is not extensible to a pair of occasionally weakly compatible maps, even if defined over a discrete metric space.

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
Full Text: Link