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 xn=αnxn−1+βnSnxn−1+γnTnxn,n∈N where Tn=TnmodN,Sn=SnmodN, 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].