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, nεN where Tn=TnmodN,. Sn=SnmodN, NεN. 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]. © 2010 Elsevier Ltd.