Abstract: The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.

Key words: Lipschitzian pseudo-contraction semi-group, demi-closed principle, common fixed point, Opial condition, strongly pseudo-contraction mapping, implicit