CONVERGENCE OF THE ITERATION PROCESS FOR NONEXPANSIVE MAPPING SEQUENCES

作     者：黄家琳 邓磊 

作者机构：西南师大数学系 

出 版 物：《宜宾学院学报》 (Journal of Yibin University)

年 卷 期：1997年第2期

页      面：1-5页

学科分类：0401[教育学-教育学] 04[教育学] 

主　　题：and phrases Iteraion method nonespansive mapping. 

摘      要：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≤t1and (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.