Abstract and Applied Analysis
Volume 4 (1999), Issue 1, Pages 49-59
Nonlinear ergodic theorems for a semitopological semigroup of
non-Lipschitzian mappings without convexity
1Department of Mathematics, Yangzhou University, Yangzhou 225002, China
2Department of Mathematics, Kyungnam University, Kyungnam 631-701, Masan, Korea
Received 2 February 1999
Copyright © 1999 G. Li and J. K. Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a semitopological semigroup, a nonempty subset of a
real Hilbert space , and a representation of as asymptotically nonexpansive type mappings of into itself. Let for each and . In this paper, we prove that is nonempty for each if and only if there exists a unique nonexpansive retraction of into such that for all and for every . Moreover, we prove the ergodic convergence theorem for a semitopological semigroup of non-Lipschitzian mappings without convexity.