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

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Abstract

The purpose of this paper is to study the following iteration process xn=αnxn1+βnSnxn1+γnTnxn,nN where Tn=TnmodN,Sn=SnmodN, NN. 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].

Keywords

Lipschitzian pseudocontractive mappings
Iteration process
Strong and weak convergence
Common fixed points

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