Convergence of sequence of nonexpansive mapping
Xueqin Wang · 2005
Let D is a subset of the mormed space X,Tn∶D→X is a sequence of o perators satisfying ‖Tix-Tjy‖‖x-y‖ for all x,y∈D and i,j1.Given a sequ ence in D and real sequences,satistying the following conditions:(a) 0tnt 1 且tn=∞;(b) 0sn1且sn∞;(c) xn+1=tnTn(snTnxn+(1-sn)xn)+(1-tn)xn n=1,2,....We prove if is bounded,then ‖Tnxn-xn‖= 0..and show the condition to quarantee the Ishikawa iterative process weakly and strongly convergent to th e common fixed point of.