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...
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171299223770 |
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| _version_ | 1849307015105478656 |
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| author | Young-Ye Huang Chung-Chien Hong |
| author_facet | Young-Ye Huang Chung-Chien Hong |
| author_sort | Young-Ye Huang |
| collection | DOAJ |
| description | 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). |
| format | Article |
| id | doaj-art-25849f9ccbf842d8a2f96304c2f84336 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-25849f9ccbf842d8a2f96304c2f843362025-08-20T03:54:52ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-0122237738610.1155/S0161171299223770Common fixed point theorems for semigroups on metric spacesYoung-Ye Huang0Chung-Chien Hong1Department of Mathematics, National Cheng Kung University, Tainan 70101, TaiwanDepartment of Mathematics, National Cheng Kung University, Tainan 70101, TaiwanThis 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).http://dx.doi.org/10.1155/S0161171299223770Fixed pointleft reversibleupper semicontinuous. |
| spellingShingle | Young-Ye Huang Chung-Chien Hong Common fixed point theorems for semigroups on metric spaces International Journal of Mathematics and Mathematical Sciences Fixed point left reversible upper semicontinuous. |
| title | Common fixed point theorems for semigroups on metric spaces |
| title_full | Common fixed point theorems for semigroups on metric spaces |
| title_fullStr | Common fixed point theorems for semigroups on metric spaces |
| title_full_unstemmed | Common fixed point theorems for semigroups on metric spaces |
| title_short | Common fixed point theorems for semigroups on metric spaces |
| title_sort | common fixed point theorems for semigroups on metric spaces |
| topic | Fixed point left reversible upper semicontinuous. |
| url | http://dx.doi.org/10.1155/S0161171299223770 |
| work_keys_str_mv | AT youngyehuang commonfixedpointtheoremsforsemigroupsonmetricspaces AT chungchienhong commonfixedpointtheoremsforsemigroupsonmetricspaces |