Strong Convergence of an Implicit Iteration for a Finite Family of Non-self Nonexpansive Mappings
Zhou Hai-yun · Shuxue de shijian yu renshi · 2007
Suppose K is a nonempty closed convex nonexpansive retract of a uniformly convex Banach space E with P as a nonexpansive retraction.Let {Ti:i=1,2,…N}:K→E be N nonexpansive mappings with F(T)=∩ from i=1 to N F(Ti)≠■.Define a sequence {xn} as follows:x0∈K,xn=P(αnxn-1+(1-αn)TnP[βnxn-1+(1-βn)Tnxn]),n≥1,where {αn} and {βn} are real sequences in for some δ∈(0,1).If {Ti:i=1,2,…,N} satisfy the condition(B),the strong convergence of {xn} to some point x*∈F(T) is obtained.