Abstract and Applied Analysis
Volume 5 (2000), Issue 3, Pages 147-158

Nonlinear ergodic theorems for asymptotically almost nonexpansive curves in a Hilbert space

Gang Li1 and Jong Kyu Kim2

1Department of Mathematics, Yangzhou University, Yangzhou 225002, China
2Department of Mathematics, Kyungnam University, Masan, Kyungnam 631-701, Korea

Received 3 May 2000

Copyright © 2000 Gang Li and Jong Kyu 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.


We introduce the notion of asymptotically almost nonexpansive curves which include almost-orbits of commutative semigroups of asymptotically nonexpansive type mappings and study the asymptotic behavior and prove nonlinear ergodic theorems for such curves. As applications of our main theorems, we obtain the results on the asymptotic behavior and ergodicity for a commutative semigroup of non-Lipschitzian mappings with nonconvex domains in a Hilbert space.