A common fixed point of weakly commuting multivalued mappings. (English) Zbl 0664.54031

Kaneko, Hideaki

Math. Jap. 33, No. 5, 741-744 (1988).

Let (X,d) be a metric space and let CB(X) denote the family of all closed and bounded subsets of X. It is well known that CB(X) is a metric space with the Hausdorff metric H. Following the author we call the mappings f and g from X into CB(X) weakly commuting, if H(fg(x),gf(x))\(\leq H(f(x),g(x))\), for every \(x\in X\) provided H(fg(x),gf(x)) is defined. A theorem on a common fixed point for two weakly commuting maps is proved.

Reviewer: L.Gorniewicz

MSC:

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

Keywords:

weakly commuting