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Common fixed point theorems for semigroups on metric spaces

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  • Young-Ye Huang
  • Chung-Chien Hong

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 ) .

Suggested Citation

  • Young-Ye Huang & Chung-Chien Hong, 1999. "Common fixed point theorems for semigroups on metric spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 22, pages 1-10, January.
  • Handle: RePEc:hin:jijmms:372813
    DOI: 10.1155/S0161171299223770
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