广义Lipschitz增生算子方程的具有误差的Ishikawa迭代的收敛性和稳定性

The Convergence and Stability of Ishikawa Iteration with Errors for Generalized Lipschitz Accretive Operator Equations

设E是任意实Banach空间,T:E→E是Lipschitz增生算子,利用包含通常的Lipschitz映象和值域有界映象在内的广义Lipschitz映象,在没有条件limβn=0之下,在Banach空间中证明了含广义Lipschitzn→∞增生算子T的非线性方程x+Tx=f具有误差的Ishikawa迭代序列强收敛性,并在适当条件下证明了迭代序列的稳定性.

Let E be an arbitrary real Banach space and T:E→E an generalized Lipschitz continuous accretive operator. In this paper, by using the concept of generalized Lipschitz continuous accretive operator, including the Lipschitz mappings and rangebounded mapping, under certain conditions without limβn=0, we prove that the Ishikawa iterative methods with errors converge strongly to solution of the nonlinear equation x+Tx=f (f∈E),n→∞ of the generalized Lipschitz continuous accretive operator. We also prove the stability of the iteration.