Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces. (1997) - Jung, Jong Soo
Abstract : LetC be a nonempty closed convex subset of a uniformly convex Banach spaceE with a Fréchet differentiable norm, G a right reversible semitopological semigroup, and𝒮 = { S ( t ) : t ∈ G } a continuous representation ofG as mappings of asymptotically nonexpansive type ofC into itself. The weak convergence of an almost-orbit{ u ( t ) : t ∈ G } of𝒮 = { S ( t ) : t ∈ G } onC is established. Furthermore, it is shown that ifP is the metric projection ofE onto setF ( S ) of all common fixed points of𝒮 = { S ( t ) : t ∈ G }, then the strong limit of the net{ P u ( t ) : t ∈ G } exists.