Abstract and Applied Analysis
Volume 5 (2000), Issue 3, Pages 147-158
doi:10.1155/S1085337500000312
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
Abstract
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.