Nonlinear Mean Ergodic Theorems for Semigroups in Hilbert Spaces

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.