Common Fixed Point Theorems for Semigroups on Metric Spaces
نویسندگان
چکیده
This paper consists of two main results. The first one shows that if S is a left reversible semigroup of selfmaps on a complete metric space (M,d) such that there is a gauge function φ for which d(f(x),f (y)) ≤ φ(δ(Of (x,y))) for f ∈ S and x,y in M , where δ(Of (x,y)) denotes the diameter of the orbit of x,y under f , then S has a unique common fixed point ξ in M and, moreover, for any f in S and x in M , the sequence of iterates {fn(x)} converges to ξ. The second result is a common fixed point theorem for a left reversible uniformly Lipschitzian semigroup of selfmaps on a bounded hyperconvex metric space (M,d).
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