Common fixed point theorems for semigroups on metric spaces

Young-Ye Huang and Chung-Chien Hong

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-10

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 ( O f ( x , y ) ) ) for f ∈ S and x , y in M , where δ ( O f ( 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 { f n ( 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 ) .

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:372813

DOI: 10.1155/S0161171299223770

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