带误差的Ishikawa迭代程序的收敛性及其应用

Convergence of Ishikawa iteration procedures with errors and application

得到了任意实Banach空间中带误差的Ishikawa迭代程序逼近Lipschitz强伪压缩算子的不动点与Lipschitz强增生算子的方程解的一般性定理 (允许limn→∞αn≠ 0或limn→∞βn≠ 0 ) ,并用不同于通常的方法证明了任意实Banach空间中的Ishikawa迭代程序关于Lipschitz强伪压缩算子 (或强增生算子 )

The general theorem on the Ishikawa iterative approximation with errors of fixed point for Lipschitz strongly pseudo-contractive operators and solution for Lipschitz strongly accretive operators is obtained in arbitrary real Banach spaces(permitting limn→∞α n≠0 or limn→∞β n≠0 ). As the direct application, using unusual methods, it is proved that certain Ishikawa iteration procedures are stable with respect to Lipschitz strongly pseudo-contractive operators(or strongly accretive operator). These results generalize or extend the recent corresponding results.