Nonlinear Mean Ergodic Theorems for Semigroups in Hilbert Spaces

Research Article Nonlinear Mean Ergodic Theorems for Semigroups inHilbert Spaces

Let K be a nonempty subset of a Hilbert space , where K is not necessarily closed and convex. A family Γ= {T(t); t ≥ 0} of mappings T(t) is called a semigroup on K if (S1) T(t) is a mapping from K into itself for t ≥ 0, (S2) T(0)x = x and T(t+ s)x = T(t)T(s)x for x ∈ K and t,s≥ 0, (S3) for each x ∈ K , T(·)x is strongly measurable and bounded on every bounded subinterval of [0,∞). Let Γ be a se...

Mean Ergodic Theorems for C0 Semigroups of Continuous Linear Operators

In this paper we obtained mean ergodic theorems for semigroups of bounded linear or continuous affine linear operators on a Banach space under non-power bounded conditions. We then apply them to the wave equation and the system of elasticity to show that the mean of their solutions converges to their equilibriums.

Ergodic Theorems and Perturbations of Contraction Semigroups

We provide sufficient conditions for sums of two unbounded operators on a Banach space to be (pre-)generators of contraction semigroups. Necessary conditions and applications to positive semigroups on Banach lattices are also presented.

Nonlinear Ergodic Theorems for Asymptotically Almost Nonexpansive Curves in a Hilbert Space

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-Lips...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition