Ergodic Theorems For Semigroups Research Articles

Fixed point, convergence and nonlinear ergodic theorems for some semigroups in Hilbert spaces

In this paper, we first introduce some semigroups of mappings called quasi-nonexpansive, nonspreading, hybrid, TJ-1, TJ-2, and generalized hybrid semigroup. Then, using the theory of invariant means, we prove fixed point theorems, weak convergence theorem of Mann’s type and generalized nonlinear ergodic theorem for such semigroups in a Hilbert space. Furthermore, we prove a strong convergence theorem of Halpern’s type for the proposed semigroups in a Hilbert space. The results presented in this paper mainly extend and improved some well-known results in the literature.

Mean ergodic theorem for semigroups of linear operators in multi-Banach spaces

Abstract In this paper, by using Rodé’s method, we extend Yosida’s theorem to semigroups of linear operators in multi-Banach spaces. MSC:39A10, 39B72, 47H10, 46B03.

Nonlinear Mean Ergodic Theorems for Semigroups in Hilbert Spaces

Let be a nonempty subset (not necessarily closed and convex) of a Hilbert space and let be a semigroup on and let be an almost orbit of . In this paper, we prove that every almost orbit of is almost weakly and strongly convergent to its asymptotic center.

Weak almost periodicity and the strong ergodic limit theorem for periodic evolution systems

The first ergodic theorems for semigroups of nonlinear operators date back to work done by J. B. Baillon Cl, 23 in 1975, 1976, where he proved (in [2]) that /I.I/-lim.,, (l/T) j’t S(i) x dt exists for an odd (nonlinear) contraction semigroup (S(t)), a 0 in real Hilbert space. In subsequent years, various authors have extended his results to motions and almost-orbits of nonlinear strongly continuous semigroups in uniformly convex Banach spaces; e.g., see [4-10, 22-24, 26, 27, 30, 31, 33, 351, as well as [4, 10, 241 for yet further references. These results apply to strong and integral solutions of the (quasi-autonomous) nonlinear Cauchy problem

An Abelian Ergodic Theorem for Semigroups in L p Space

An Abelian Ergodic Theorem for Semigroups in L p Space

Ergodic theorems for semi-groups in $L_{p}$, $1<p<\infty $

Ergodic theorems for semi-groups in $L_{p}$, $1<p<\infty $

An ergodic theorem for semigroups

Introduction. The purpose of this paper is to prove a maximal ergodic theorem (Theorem 1) for continuous semigroups of positive contractions. This result is a continuous extension of the maximal ergodic theorem first introduced by Brunel [4] and then generalized in [1] and [2]. The continuous version of Chacon-Ornstein's ratio ergodic theorem which can be proved directly [7], as noted by the referee, is also a corollary of our result. This continuous version of Chacon-Ornstein's theorem was also proved by Berk [3] by different methods.

An Ergodic Theorem for Semigroups

An Ergodic Theorem for Semigroups