International Journal of Mathematics and Mathematical Sciences 
Volume 20 (1997), Issue 1, Pages 51-60
doi:10.1155/S0161171297000094

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

Abstract

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.