Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces. (1997) - Jung, Jong Soo; Park, Jong Yeoul; Park, Jong Seo
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.