## 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.

### MSC:

 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems

### Keywords:

compatible maps; occasionally weakly compatible maps

Zbl 1175.41026
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