Jung, Jong Soo; Park, Jong Yeoul; Park, Jong Seo Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces. (English) Zbl 0891.47047 Int. J. Math. Math. Sci. 20, No. 1, 51-60 (1997). Summary: 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 \({\mathcal S}= \{S(t): t\in G\}\) a continuous representation of \(G\) as mappings of asymptotically nonexpansive type of \(C\) into itself. The weak convergence of an almost-orbit \(\{u(t): t\in G\}\) of \({\mathcal S}\) on \(C\) is established. Furthermore, it is shown that if \(P\) is the metric projection of \(E\) onto the set \(F({\mathcal S})\) of all common fixed points of \({\mathcal S}\), then the strong limit of the net \(\{Pu(t): t\in G\}\) exists. MSC: 47H20 Semigroups of nonlinear operators 47H10 Fixed-point theorems 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. Keywords:uniformly convex Banach space; Fréchet differentiable norm; right reversible semitopological semigroup; continuous representation; mappings of asymptotically nonexpansive type; weak convergence of an almost-orbit; common fixed points PDFBibTeX XMLCite \textit{J. S. Jung} et al., Int. J. Math. Math. Sci. 20, No. 1, 51--60 (1997; Zbl 0891.47047) Full Text: DOI EuDML