Convergence of a generalized iteration process for two finite families of Lipschitzian pseudocontractive mappings

The purpose of this paper is to study the following iteration process x n = α n x n − 1 + β n S n x n − 1 + γ n T n x n , n ∈ N where T n = T n mod N , S n = S n mod N , N ∈ N . We prove a necessary and sufficient condition to obtain a strong convergence result. We also prove some other strong and weak convergence theorems for this iteration process for approximating a common fixed point of two finite families of Lipschitzian pseudocontractive mappings. Our results extend, improve and unify the corresponding results of Chen, Song and Zhou (2006) [8], Hao (2008) [11], Li, He and Zhao (2009) [9].