Newton-Steffensen型迭代在广义Lipschitz条件下的半局部收敛性

On semilocal convergence for the Newton-Steffensen method under generalized Lipschitz conditions

研究了一种Newton-Steffensen型迭代法求解Banach空间中非线性算子方程的半局部收敛问题.当非线性算子F的一阶导数满足广义Lipschitz条件时,得到了Newton-Steffensen法的三阶收敛性.所得结果推广了相关文献的结果.

The present paper concerns with the semilocal convergence problems for a Newton-Steffensen iterative method in Banach spaces.When the Fréchet derivative of the nonlinear operator F satisfies a generalized Lipschitz condition,a new semilocal convergence result is obtained for the Newton-Steffensen method.Our result extends the corresponding results in existing works.