TY - JOUR
T1 - Convergence of a generalized iteration process for two finite families of Lipschitzian pseudocontractive mappings
AU - Khan, Safeer Hussain
AU - Yildirim, Isa
AU - Ozdemir, Murat
PY - 2011/3/1
Y1 - 2011/3/1
N2 - 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.
AB - 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.
KW - Common fixed points
KW - Iteration process
KW - Lipschitzian pseudocontractive mappings
KW - Strong and weak convergence
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U2 - 10.1016/j.mcm.2010.10.007
DO - 10.1016/j.mcm.2010.10.007
M3 - Article
SN - 0895-7177
VL - 53
SP - 707
EP - 715
JO - Mathematical and Computer Modelling
JF - Mathematical and Computer Modelling
IS - 5-6
ER -