On Common Fixed Points of Weakly Commuting Mappings and Set - Valued Mappings
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چکیده
ABS]RACT. Our main theorem establishes the uniqueness of the common fixed point of tw set-valued mappings and of two single-valued mappings defined on a complete metric space, under a contractive condition and a weak commutativity concept. This improves a theorem of the second author. Let (X,d) be a complete metric space and let B(X) be the set of all nonempty, bounded subsets of X As in [I], let (A,B) be the function defined by (A,B) sup {d(a,b) a A, b B} for all A, B in B(X). If A consists of a single point a we write 6(A,B) (a,B) and if B also consists of a single point b we write (A,B) d(a,b) It follows immediately from the definition that 6(A,C) + 6(C,B) for all A B C in B(X). We say that a subset A of X is the limit of a sequence {A of nonempty sub-n sets of X if each point a in A is the limit of a convergent sequence {a }, where n a is in A for n 1,2 and if for arbitrary
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تاریخ انتشار 1984