渐近拟非扩张映射的Ishikawa迭代序列(英文)

Ishikawa Iterative Sequences for Asymptotically Quasi-nonexpansive Mappings

设E为Banach空间,T是E到E上的渐近拟非扩张映射,T的不动点集合F(T)非空.对任意的x0∈E,如Ishikawa迭代序列定义xn+1=(1-tn)xn+tnTnyn,yn=(1-sn)+snTnxn, tn,sn∈[0,1], n=1,2,3…在不要求T具有连续的条件下,给出并证明了序列{xn}收敛到T的不动点的充分必要条件,我们的定理改进了近期的相应结果.

Let E be a Banach space, T:E→E an asymptotically quasinonexpansive mapping of E.F(T) denotes the set of fixed points of T and F(T) is nonempty. For any given x0∈E, the Ishikawa sequence {xn} is defined byxn+1=(1-tn)xn+tnTnyn,yn=(1-sn)+snTnxn,tn,sn∈,n=1,2,3....In this paper, a sufficient and necessary condition for an Ishikawa iterative sequence of asymptotically quasinonexpansive mapping T to converge to a fixed point where T need not be continuous. The recently corresponding results are improved by our theorems.