渐近拟非扩张映射的Ishikawa迭代序列

设E为Banach空间，T是E到E上的渐近似非扩张映射，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 tnT^nyn,yn=(1-sn) snT^nxn,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。

Ishikawa Iterative Sequences for Asymptotically Quasi-nonexpansive Mappings

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 x0∈E, the Ishikawa sequence {xn} is defined byxn+1=(1-tn)xn+tnTnyn,yn=(1-sn)+snTnxn, tn,sn∈[0,1], 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.