Asymptotic behavior of almost‐orbits of reversible semigroups of non‐Lipschitzian mappings in Banach spaces
Jong Soo Jung, Jong Yeoul Park, Jong Seo Park · International Journal of Mathematics and Mathematical Sciences · 1995
Let C be a nonempty closed convex subset of a uniformly convex Banach space E with a Fréchet differentiable norm, G a right reversible semitopological semigroup, and 𝒮 = {S(t) : t ∈ G} a continuous representation of G as mappings of asymptotically nonexpansive type of C into itself. The weak convergence of an almost‐orbit {u(t) : t ∈ G} of 𝒮 = {S(t) : t ∈ G} on C is established. Furthermore, it is shown that if P is the metric projection of E onto set F(S) of all common fixed points of 𝒮 = {S(t) : t ∈ G}, then the strong limit of the net {Pu(t) : t ∈ G} exists.