Young-Ye Huang, Chung-Chien Hong, "Common fixed point theorems for semigroups on metric spaces", International Journal of Mathematics and Mathematical Sciences, vol. 22, Article ID 372813, 10 pages, 1999. https://doi.org/10.1155/S0161171299223770
Common fixed point theorems for semigroups on metric spaces
This paper consists of two main results. The first one shows that if is a left reversible semigroup of selfmaps on a complete metric space such that there is a gauge function for which for and in , where denotes the diameter of the orbit of under , then has a unique common fixed point in and, moreover, for any in and in , the sequence of iterates converges to . The second result is a common fixed point theorem for a left reversible uniformly Lipschitzian semigroup of selfmaps on a bounded hyperconvex metric space .
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