International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1999 / Article

Open Access

Volume 22 |Article ID 372813 | 10 pages | https://doi.org/10.1155/S0161171299223770

Common fixed point theorems for semigroups on metric spaces

Received21 Dec 1995
Revised16 Feb 1998

Abstract

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 fS 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).

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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