International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 51-60

Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces

Jong Soo Jung,1 Jong Yeoul Park,2 and Jong Seo Park3

1Department of Mathematics, Dong-A University, Pusan 607-714, Korea
2Department of Mathematics, Pusan National University, Pusan 609-735, Korea
3Department of Mathematics, Graduate School, Dong-A University, Pusan 607-714, Korea

Received 15 February 1994; Revised 25 October 1995

Copyright © 1997 Jong Soo Jung et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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):tG} a continuous representation of G as mappings of asymptotically nonexpansive type of C into itself. The weak convergence of an almost-orbit {u(t):tG} of 𝒮={S(t):tG} 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):tG}, then the strong limit of the net {Pu(t):tG} exists.