关于Banach空间中增生算子方程的迭代法收敛率估计(英文)

On the Convergence Rate Estimates of Iteration Methods for Equations Involving Accretive Operators in Banach Spaces

本文研究Banach空间中增生算子方程的Ishikawa迭代法收敛率估计 .本文所得结果在以下方面改进和推广了刘理蔚的结果 (NonlinearAnal.4 2 ( 2 ) ( 2 0 0 0 ) ,2 71～ 2 76 ) :( 1 )以假设{αn},{βn}在不同区间上独立取值代替刘的假设limn→∞αn =limn→∞βn =0 ;( 2 )以一般的收敛率估计和几何收敛率估计代替刘的收敛率估计‖xm -x ‖ =O( 1 /m) .

The purpose of this paper is to investigate the convergence rate estimate of Ishikawa iteration method for equations involving accretive operators in Banach spaces. The results presented in this paper improve and extend Liu's result (Nonlinear Anal. 42(2)(2000),271-276) through replacing Liu's assumption that lim n→∞α n= lim n→∞β n=0 by the assumption that {α n},{β n} independently take values in the different intervals, and through replacing Liu's convergence rate estimate ‖x m-x *‖=O(1/m) by the general convergence rate estimate and the geometric convergence rate estimate.