CONVERGENCE OF THE ITERATION PROCESS FOR NONEXPANSIVEMAPPING SEQUENCES

摘要

cqvip:Let D be a subset of a normed space X and Tn:D→X with || Tix-Tjy ||≤|| x-y || for all x,y∈D and for all i,j≥1. Given a sequence {xn} in D and two real sequences {tn} and (βn) satisfying (i)0≤tn≤t<1and (sum from n=1 to ∞(1/n))tn=∞(ii)0≤sn≤1and (sum from n=1 to ∞(1/n))sn<∞(iii)xn+1=tnTn(snTnxn=(1-sn)xn))+(1-tn)xn,n=1,2,3……We prove that if {xn} is bounded, then Hm || Tnxn-xn||=0. The conditions on D,X and Tn are shown which guarantee the weak and storng convergence of the Ishikawa iteration process to a common fixed point of Tn.1991 Mathematics Subject Classification. Primary 47H10, Secondary 40A05.