Fixed Point Theory and Applications 
Volume 2007 (2007), Article ID 73246, 9 pages
doi:10.1155/2007/73246
Research Article

Nonlinear Mean Ergodic Theorems for Semigroups in Hilbert Spaces

Seyit Temir and Ozlem Gul

 Department of Mathematics, Arts and Science Faculty, Harran University, Sanliurfa 63200, Turkey
Received 26 December 2006; Accepted 4 April 2007

Recommended by Nan-Jing Huang

Abstract

Let K be a nonempty subset (not necessarily closed and convex) of a Hilbert space and let Γ={T(t);t≥0} be a semigroup on K and let α(.):[0,∞)→K be an almost orbit of Γ. In this paper, we prove that every almost orbit of Γ is almost weakly and strongly convergent to its asymptotic center.