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

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

weakly commuting