一致L-Lipschitz的渐近拟伪压缩型映象迭代收敛的充要条件

设E是任意的实Banach空间,C是E的非空凸子集(C可以是E的无界子集),T:C→C是→致L-Lipschitz的渐近拟伪压缩型映象,在对参数的一些限制条件下,该文给出了带误差的修改的Ishikawa迭代序列强收敛于T的不动点的充要条件.

A Necessary and Sufficient Condition for the Iterative Sequence Convergence to the Fixed Point of Uniformly L-Lipschitz Asymptotically Quasi Pseudo-Contractive Type Mapping

Suppose $\Bbb E$ is a real Banach space, $\Bbb C$is a nonempty convex subset of $\Bbb E$($\Bbb C$ may be a unbounded subset of$\Bbb E$), $T:\Bbb C\rightarrow \Bbb C$ is a uniformly $L$-Lipschitzian asymptotically quasi pseudo-contractive type mapping, under some restrictive conditions on the parameters, anecessary and sufficient condition is given for the modified Ishikawa iterative sequence with error to converge strongly to a fixed point of $T$.