A Nonlinear Ergodic Theorem for a Reversible Semigroup of Lipschitzian Mappings in a Hilbert Space

Nonlinear Ergodic Theorems for a Semitopological Semigroup of Non-lipschitzian Mappings without Convexity

Let G be a semitopological semigroup, C a nonempty subset of a real Hilbert space H , and = {Tt : t ∈ G} a representation of G as asymptotically nonexpansive type mappings of C into itself. Let L(x)= {z ∈H : infs∈G supt∈G ‖Ttsx−z‖ = inf t∈G ‖Ttx−z‖} for each x ∈ C and L( )= ⋂x∈C L(x). In this paper, we prove that ⋂s∈G conv{Ttsx : t ∈ G}⋂L( ) is nonempty for each x ∈ C if and only if there exist...

A Weak Ergodic Theorem for Infinite Products of Lipschitzian Mappings

Let K be a bounded, closed, and convex subset of a Banach space. For a Lipschitzian self-mapping A of K , we denote by Lip(A) its Lipschitz constant. In this paper, we establish a convergence property of infinite products of Lipschitzian self-mappings of K . We consider the set of all sequences {At}t=1 of such selfmappings with the property limsupt→∞ Lip(At) ≤ 1. Endowing it with an appropriate...

A composite explicit iterative process with a viscosity method for Lipschitzian semigroup in a smooth Banach space

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

An Ergodic Theorem for a Noncommutative Semigroup of Linear Operators

Introduction. The question of ergodicity of a semigroup of bounded linear operators on a Banach space has been reduced, by Alaoglu and Birkhoff [l],1 Day [2, 3], and Eberlein [4], to the study firstly of the ergodicity of the semigroup itself and secondly, of the ergodicity of each element of the Banach space with respect to this ergodic semigroup. In the case of a bounded and commutative semig...