Weak convergence theorem for Lipschizian pseudocontraction semigroups in Banach spaces

The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontraction semigroups in general Banach spaces. The results presented in this paper extend and improve the corresponding results of Zhou [Nonlinear Anal., 68, 2977–2983 (2008)], Chen, et al. [J. Math. Anal. Appl., 314, 701–709 (2006)], Xu and Ori [Numer. Funct. Anal. Optim, 22, 767–773 (2001)] and Osilike [J. Math. Anal. Appl., 294, 73–81 (2004)].