Common fixed point theorems for semigroups on metric spaces
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...
| Published in: | International Journal of Mathematics and Mathematical Sciences |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1999-01-01
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| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171299223770 |
| Summary: | 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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| ISSN: | 0161-1712 1687-0425 |