增生型非线性方程的具混合误差项的Ishikawa迭代程序的收敛性和稳定性

Convergence and Stability of the Ishikawa Iteration Procedures with Mixed Errors for Nonlinear Equations of the Accretive Type

设X是任意Banach空间,T:X→X是Lipschitz增生算子,Sx=f-Tx, x∈X.在没有条件limαn=limβn=0之下,证明了具混合误差项的Ishikawa迭代程序是收敛的和几乎S 稳定的.相关地还得n→∞n→∞到了非线性强增生型算子方程Tx=f解的具混合误差项的Ishikawa迭代程序的收敛性和稳定性结果,所得结果改进和推广了近期的一些相关结果.

Let X be an arbitrary real Banach space, T:X→X be a Lipschitz accretive operator and Sx=f-Tx for all x∈X. Under the lack of the condition  lim n→∞α n= lim n→∞β n=0, it is proved that certain Ishikawa iteration procedures with mixed errors are both convergent and almost S stable. Related results deal with the convergence and stability of the Ishikawa iteration procedures with mixed errors for iterative approximation of solutions of the nonlinear strongly aceretive operator equation Tx=f. Our results extend and improve some recent corresponding results.