A note on occasionally weakly compatible maps. (English) Zbl 1181.54045

Al-Thagafi, M. A.; Shahzad, N.

Int. J. Math. Anal., Ruse 3, No. 1-4, 55-58 (2009).

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.

Reviewer: Salvatore Sessa (Napoli)

MSC:

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

Keywords:

compatible maps; occasionally weakly compatible maps

Citations:

Zbl 1175.41026