Published online by Cambridge University Press: 17 April 2009
We study some convergence of two kinds of implicit iteration processes for approximating common fixed points of a pseudo-contractive semigroup in uniformly convex Banach spaces with uniformly Gateaux differential norms. As special cases, we get some convergence of the implicit iteration processes for approximating common fixed points of a nonexpansive semigroup in uniformly smooth Banach spaces and give a positive answer to an open problem proposed by Xu in Bull. Austral. Math. Soc. (2005). The results presented in this paper generalise some corresponding results from Osilike in Panamer. Math. J. (2004), Suzuki in Proc. Amer. Math. Soc. (2002) and Xu in Bull. Austral. Math. Soc. (2005).