Research Article Nonlinear Mean Ergodic Theorems for Semigroups inHilbert Spaces
نویسندگان
چکیده
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 semigroup on K . Then F = {x ∈ K : T(t)x = x, t ≥ 0} is said to be fixedpoints set of Γ. We state a condition introduced by Miyadera [1]. If, for every bounded set B ⊂ K , v ∈ K , and s≥ 0, there exists a δs(B,v)≥ 0 with lims→∞ δs(B,v)= 0 such that
منابع مشابه
Non-linear ergodic theorems in complete non-positive curvature metric spaces
Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...
متن کاملA Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition
متن کامل
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.
متن کاملNonlinear 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...
متن کاملFixed point theorems for some new nonlinear mappings in Hilbert spaces
* Correspondence: [email protected]. edu.tw Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan Full list of author information is available at the end of the article Abstract In this paper, we introduced two new classes of nonlinear mappings in Hilbert spaces. These two classes of nonlinear mappings contain some important classes of nonlinear mappings, l...
متن کامل